SB    E7fl 


iURAL  ARITHIvl 

CALFEE 


IN  MEMORIAM 
FLOR1AN  CAJORI 


RURAL  ARITHMETIC 


A  COURSE  IN  ARITHMETIC INTEOT}:£D>  Ttf  ^T 
CHILDREN  TO  THINKING  ;J^ND  MGtJRING 
ON  HOME  AND  ITS  IMPROVEMENT 


BY 


JOHN  E.  CALFEE 


PROFESSOR  OF  MATHEMATICS,  BEREA  COLLEGE  NORMAL 
BEREA,  KENTUCKY 


GINN  AND  COMPANY 

BOSTON  •  NEW  YORK  •  CHICAGO  •  LONDON 


COPYRIGHT,  1913,  BY 
JOHN  E.  CALFEE 


ALL  RIGHTS  RESERVED 
814.1 


CAJORI 


G1NN  AND  COMPANY-  PRO- 
PRIETORS •  BOSTON  •  U.S.A. 


PREFACE 

To  a  large  extent  the  old-time  arithmetics  were  made  and 
taught  with  a  view  to  preparing  pupils  for  passing  exami- 
nations. Expressed  or  implied,  the  theory  was  that  the  func- 
tion of  the  elementary  school  was  to  prepare  for  college. 
The  child  who  was  never  to  enter  college  was  looked  upon 
as  a  very  unfortunate  being ;  he  was  reckoned  as  of  little 
promise.  Consequently  no  definite  provision  was  made  for 
those  who  must  toil  and  do  the  world's  work  by  the  sweat 
of  the  brow ;  they  were  set  adrift  to  take  up  the  world's 
industrial  and  commercial  work  with  almost  no  preparation 
leading  to  economic  and  industrial  efficiency.  As  a  result 
the  soil  has  been  abused  and  worn  out,  much  of  the  timber 
wasted,  and  many  once  fertile  farms  abandoned. 

The  purpose  of  this  book  is  to  touch  the  important  phases 
of  farm  management.  The  problems  are  real  and  practical, 
taken  from  everyday  farm  life ;  the  information  given  is 
reliable  and  valuable,  and  can  be  used  to  increase  the  profits 
in  farming.  The  country  boy  and  girl  are  taught  in  terms 
of  their  immediate  surroundings  ;  they  are  given  a  chance  to 
solve  problems  in  which  they  and  their  parents  are  vitally 
interested.  The  management  of  the  farm  is  made  an  at- 
tractive and  intelligent  subject  for  conversation  around 
the  home  fireside  during  the  long  winter  evenings.  A 
sane,  practical  business  outlook  upon  the  administration  of 
farm  affairs  will  develop  in  the  children  a  broad  view  of 
the  unbounded  opportunities  which  the  farm  offers  for  the 
accumulation  of  wealth  and  happiness.  The  farmers'  children 

iii 


911242 


iv  PREFACE 

are  entitled  to  an  education  that  will  give  them  a  fair  chance 
of  remaining  on  the  farm  as  successful  farmers,  and  to  this 
end  I  submit  this  book. 

The  author  desires  to  thank  sincerely  his  students,  and 
also  Professors  Charles  D.  Lewis,  E.  C.  Seale,  John  F.  Smith, 
F.  0.  Clark,  J.  A.  Burgess  (architect  and  builder),  Dr.  W.  L. 
Heizer  of  the  Kentucky  State  Board  of  Health,  and  President 
Frost  of  Berea  College,  for  their  advice  and  criticism. 

J.  E.  C. 


CONTENTS 

PAGE 

FUNDAMENTAL  PROCESSES  ...............  1 

Rapid  Addition     ..................  1 

Subtraction    ....................  5 

Multiplication    .............    ......  8 

Division      .....................  11 

DECIMALS    ......................  13 

EDUCATION  AND  THRIFT     .........    .    .....  18 

Educated  Labor    ..................  18 

Training  for  Head  and  Hand   .............  19 

Idleness,  Carelessness,  and  Waste  of  Machinery    .....  21 

Produce,  Grain,  and  Stock  Market  ...........  23 

Poultry  Problems  ..................  25 

Spraying    ...........    ..........  27 

The  Value  of  Birds  to  Farmers    ............  29 

PRACTICAL  MEASUREMENTS     ..............  30 

Judging  Distance  and  Surface      ............  30 

Lumber  Measure  ..................  31 

Measuring  Lumber  in  the  Log      ............  33 

Cordwood,  Stove  Wood,  and  Coal    ...........  34 

Liquid  Measure      ..................  36 

37 


Land  Measure    ...................  39 

Areas  of  States  ...................  42 

Papering    .....................  43 

Carpeting  .....................  44 

CONSERVATION  OF  THE  SOIL  ..............  45 

Soil  Erosion   ....................  45 

Tax  upon  the  Soil  by  Different  Crops  ..........  46 

The  Cost  of  Restoring  Plant  Food  to  the  Soil      ......  47 

v 


vi  CONTENTS 

PAGE 

The  Comparative  Value  of  Manures 49 

Mixing  Fertilizers  on  the  Farm .  50 

Drainage 53 

HOUSEHOLD  AND  HEALTH  PROBLEMS 54 

Sewing 54 

Food 55 

Health  and  Sanitation 58 

GROWING  CROPS 62 

Selecting  Seed  Corn •  .  62 

Testing  Seed  Corn 64 

Cost  of  Growing  Corn  on  Rough  Land *    .    .    .  67 

Cost  of  Growing  Corn  on  Smooth  Land 68 

Cost  of  Growing  Wheat 69 

Cost  of  Growing  Cotton 69 

ESTIMATION  OF  CROPS  IN  THE  BULK 71 

Corn 71 

Hay 72 

Apples  and  Potatoes 73 

STOCK  AND  FEED  PROBLEMS 75 

Kinds  and  Quantities  of  Feed 75 

The  Dairy 79 

Silos 81 

.  Cattle  and  Hog  Problems 81 

Meat  Problems 84 

TRANSPORTATION 85 

The  Cost  of  Bad  Roads 85 

BUILDING  PROBLEMS 90 

Weatherboarding 90 

Shingling .  91 

Metal  Roofing 92 

Flooring 93 

Cutting  Rafters 94 

Stonework  and  Brickwork      97 

Painting 101 


CONTENTS  vii 

PAGE 

MACHINE,  SHOP,  AND  DRAFT  PROBLEMS 102 

Shop  Problems 102 

Problems  with  the  Lever 103 

General  Problems 105 

BUSINESS  PROBLEMS 106 

Borrowing  Money  from  Individuals 106 

Interest    .    .    . 106 

Using  the  Bank 107 

Checks 107 

Certified  Checks 108 

Borrowing  from  Banks 108 

The  Six  Per  Cent  Method  of  Finding  Interest    ....  110 

The  Day  Method  of  Finding  Interest Ill 

Discounting  Notes 113 

Paying  Cash  for  Goods 114 

State  and  Local  Taxes 115 

i 

TABLES  OF  WEIGHTS  AND  MEASURES                                     ,  118 


RURAL  ARITHMETIC 

FUNDAMENTAL  PROCESSES 

1.  The  ability  to  add,  subtract,  multiply,  and  divide,  rapidly 
and  accurately,  is  at  the  foundation  of  all  satisfactory  prog- 
ress in  the  study  of  arithmetic.  A  large  part  of  the  errors  in 
business  calculations  are  caused  by  illegible  figures  that  are 
placed  in  irregular  columns  for  addition.   More  stress  should 
be  placed  upon  making  neat,  legible  figures  of  uniform  size. 

2.  Dictation  exercises  in  writing  numbers  should  be  given 
until  the  pupil  can  write  numbers  rapidly,  placing  units  of 
the  same  order  in  the  same  vertical  column. 

3.  Much  practice  should  be  given  in  reading  at  a  glance 
numbers  consisting  of  from  two  to  five  figures,  without  nam- 
ing the  individual  figures.   A  good  reader  takes  in  a  word  at 
a  glance,  without  thinking  of  the  separate  letters  forming  the 
word ;  the  same  standard  should  be  set  for  reading  numbers. 

RAPID  ADDITION 

4.  Rapid  adding  depends  largely  upon  the  ability  to  com- 
bine instantly  two  or  more  figures  into  a  single  number. 

ORAL  EXERCISE 

Practice  naming  at  sight  the  sums  of  the  following  groups 
from  left  to  right,  from  right  to  left,  from  top  to  bottom,  and 
from  bottom  to  top,  until  the  sums  can  be  named  at  the  rate 
of  100  per  minute. 

1.  188719782285964 
192339581245311 
l 


PBOCESSES 

2.  6     8     4     7     5     3     3  '  .  <'5     7     9     8     8     6     7     4 

i\I  i   2   2  •  ]!   2-  *  •  2   5  -2'oi  2  2'  2 

3.  796784598964769 
712466265463152 

Practice  naming  at  sight  the  sums  of  the  following  groups 
until  they  can  be  named  at  the  rate  of  60  per  minute. 

4.  149648725249119 
721438466781541 


5.  653232432226117 
211221222976112 
ll>1265111221215 

6.  28'4379855733298 
475657778473533 
577399989798638 

7.  886738992645775 
954379926743124 
859839968685775 

8.  597547387786497 
997114111669143 
561461961976394 

9.  484717857445262 
734581164332526 


10.  369119523251229 
211165332811561 
251871243216228 


RAPID  ADDITION  3 

11.  984338579486346 
943171564548476 
?S5613579496696 

12.  739564534243996 
634642263425623 
335169883783396 

13.  3  3  5   6  4  9  3  8  9  -4  7  8  7  5  8 
224542577673767 

988828987839562 

14.  543228276624583 
641183129891351 
393985818874755 

5.  The  addition  of  several  numbers  arranged  in  vertical 
columns  can  be  simplified  and  rendered  much  easier  by 
thinking  only  sums. 

EXAMPLE.    35 

46          In  adding  this  column  think  "17,  24,  30,  35" ; 
77      and  not  "  9  and  8  are  17,  and  7  are  24,  and  6  are 
68      30,  and  5  are  35." 
29 

ORAL  EXERCISE 

Speaking  only  the  sums,  add  the  following : 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

385 

416 

212 

297 

911 

877 

288 

937 

276 

289 

378 

578 

762 

689 

999 

823 

425 

375 

829 

879 

879 

578 

878 

578 

738 

891 

657 

683 

648 

639 

657 

717 

897 

345 

762 

479 

532 

721 

894 

816 

365 

278 

259 

178 

891 

278 

335 

217 

FUNDAMENTAL  PROCESSES 


9.       10.       11. 

12.      13.      14. 

92,438   38,567   67,584 

98,764   34,578    35,687 

56,789   23,456   53,472 

98,745   45,384    98,756 

29,475   87,564   97,853 

25,397   98,756    98,456 

86,794   34,567   87,347 

87,564   36,574    98,564 

98,764   89,756   35,468 

96,758   98,457    46,798 

57,634   93,564   27,659 

46,534   86,534   36,575 

78,929   46,189   18,894 

61,775   10,662    18,619 

EXERCISE 

6.  Drill  on  the  following 

problems  until  correct  results 

can  be  obtained  rapidly. 

1.        2.        3. 

4.        5.        6. 

3678     8765     4578 

2871     7841     1431 

9765     4321     3287 

6354     3678     2115 

3146     3456     9976 

2789     9765     6312 

8973     7897     4521 

3436     4738     2543 

7695     6543     7894 

5678     9716     2543 

1878     7896     3786 

2143     3789     1635 

6543     8342     7312 

1713     9876     1144 

2109     8976     9543 

8947     8129     1667 

7.           8. 

9.          10. 

24,264,357     34,782,919 

27,831,641    11,223,344 

89,361,789     22,438,716 

78,397,645    55,668,899 

67,584,932     37,498,562 

26,848,973    71,158,734 

11,768,419     11,312,417 

31,913,328    25,316,275 

27,834,564     19,638,478 

95,654,724    39,423,681 

17,198,137    95,463,821 

31,216,317     41,618,755 

99,788,781    67,893,215 

13,146,184    27,377,213 

81,291,317     32,123,476 

78,945,678     16,428,746 

SUBTEACTION 


11. 

12. 

13. 

14. 

15. 

2789 

1487 

3146 

7777 

836,457 

4321 

1846 

4289 

8888 

234,532 

8456 

1531 

9744 

4563 

456,789 

7832 

2614 

8563 

2716 

123,456 

1131 

9743 

2178 

4183 

789,132 

2456 

7593 

9781 

7894 

554,437 

8937 

8171 

3456 

5533 

224,517 

6421 

7262 

8974 

4466 

811,936 

3896 

2171 

3869 

2211 

171,783 

4567 

5142 

7542 

3789 

445,688 

8947 

2591 

3476 

4567 

779,966 

8963 

1785 

7891 

8972 

154,761 

2543 

4376 

8375 

1654 

246,824 

6172 

1479 

4683 

3278 

135,781 

5891 

3215 

1575 

6473 

579,321 

7.  The  first  five  minutes  of  each  recitation  period  for 
several  days,  or  perhaps  weeks,  should  be  spent  in  drill  on 
these  exercises  and  similar  ones  prepared  by  the  teacher. 
The  time  spent  in  drill  is  regained  by  the  pupil  in  the  sav- 
ing of  his  time,  due  to  the  accuracy  and  rapidity  with  which 
he  prepares  his  lesson. 

SUBTRACTION 

8.  The  process  of  finding  the  difference   between  two 
numbers  is  made  much  easier  and  more  rapid  if  the  pupil 
is  able  to  see  at  a  glance  what  number  added  to  the  smaller 
of  two  numbers,  of  one  or  two  figures  each,  will  produce  the 
larger.   Thus,  if  13  is  to  be  subtracted  from  27,  the  pupil 
should  think  of  14,  the  number  which  added  to  13  pro- 
duces 27. 


6  FUNDAMENTAL  PKOCESSES 

ORAL   EXERCISE 

Speak  the  number  that,  added  to  the  smaller  number, 
makes  the  larger  one  in  each  of  the  following  : 

1.  354698787969599 
121235243331374 

2.  12  11  10  12  11  10  10  12  11  13.14  15  15  14  15 
J9J*_7_5_6JJ>J7_5_6_9_7J>_5_9 

3.  16  17  18  18  17  19  17  19  18  17  16  16  19  16  15 


4.  23   24    27   29   26   25   31    34   38   39   32  33  35  21   23 
^^^^1819171619141726271917 

5.  43   45   47-  49   41   40   42   44   50   54   57  59   58  55  53 


6.  52   51    53    55    57   59    61    62    63    67    69  78  75  77  71 
262739373842434529183532365837 

7.  $2.00  $5.00  $10.00  $10.00  $5.00 

$1.25  $3.75  $6.75  $3.85  $2.78 

$2.00          $20.00  $20.00  $10.00  $5.00 

$1.19  $7.18  $9.45  $4.85  $1.97 

9.  In  the  ordinary  business  transaction  of  the  store  it  is 
important  to  be  able  to  see  at  once  the  amount  of  change 
and  its  denomination.  Thus,  if  a  purchase  of  18  cents  is 
made  and  a  quarter  is  handed  to  the  merchant,  the  customer 
should  be  able  to  think  quickly  of  7  cents  as  2  pennies  and 
1  nickel,  the  change  and  its  denomination. 


SUBTRACTION  T 

ORAL  EXERCISE 

State  the  amount  of  change  and  the  denomination  in 
each  of  the  following  problems : 

Article  purchased  Amount  paid 

1.  1J.  yd.  ribbon  @  200  $1 

2.  12yd.  prints  @  50  $1 

3.  12yd.  prints  @  60  $1 

4.  3£  yd.  serge  @  500  $5 

5.  5yd.  lace  @  30  500 

6.  1  pair  shoes  @  $3.75  $10 

7.  1  hat  @  $2.25  $5 

8.  1  ax  @  900  $10 

9.  1  knife  @  550  $2 

10.  7  yd.  cotton  @  80  $1 

11.  91b.  rice  @  60  $2 

12.  3  pairs  hose  @  150  $1 

13.  7  bars  soap  @  50  500 

14.  1  bucket  @  690  $10 

15.  1  lamp  @  370  $2 

16.  1  shovel  @  130  250 

17.  2  brooms  @  350  $5 

18.  1  overcoat  @  $11.75  $20 

19.  1  pair  gloves  @  870  $5 

20.  1  suit  @  $7.25  $20 

21.  Soap,  150;  oranges,  200  $5 

22.  Sugar,  250 ;  prunes,  170  $2 

23.  Lamp,  890;  oil,  500  $5 

24.  Meal,  650;  coffee,  350  $10 

25.  Nails,  240;  wire,  $3.18  $5 


8  FUNDAMENTAL  PROCESSES 

MULTIPLICATION 

10.  There  are  72  primary  facts  of  multiplication  that 
must  be  perfectly  memorized  before  the  pupil  can  become 
skilled  in  the  process.  They  are  as  follows : 


2 

times 

2  = 

4 

3 

times 

2  = 

6 

2 

times 

3  = 

6 

3 

times 

3  = 

9 

2 

times 

4  = 

8 

3 

times 

4  = 

12 

2 

times 

5  = 

10 

3 

times 

5  = 

15 

2 

times 

6  = 

12 

3 

times 

6  = 

18 

2 

times 

7  = 

14 

3 

times 

7  = 

21 

2 

times 

8  = 

16 

3 

times 

8  = 

24 

2 

times 

9  = 

18 

3 

times 

9  = 

27 

2 

times 

10  = 

20 

3 

times 

10  = 

30 

4 

times 

2  = 

8 

5 

times 

2  = 

10 

4 

times 

3  = 

12 

5 

times 

3  = 

15 

4 

times 

4  = 

16 

5 

times 

4  = 

20 

4 

times 

5  = 

20 

5 

times 

5  = 

25 

4 

times 

6  = 

24 

5 

times 

6  = 

30 

4 

times 

7  = 

28 

5 

times 

7  = 

35 

4 

times 

8  = 

32 

5 

times 

8  = 

40 

4 

times 

9  = 

36 

5 

times 

9  = 

45 

4 

times 

10  = 

40 

5 

times 

10  = 

50 

6 

times 

2  = 

12 

7 

times 

2  = 

14 

6 

times 

3  = 

18 

7 

times 

3  = 

21 

6 

times 

4  = 

24 

7 

times 

4  = 

28 

6 

times 

5  = 

30 

7 

times 

5  = 

35 

6 

times 

6  = 

36 

7 

times 

.6  = 

42 

6 

times 

7  = 

42 

7 

times 

7  = 

49 

6 

times 

8  = 

48 

7 

times 

8  = 

56 

6 

times 

9  = 

54 

7 

times 

9  = 

63 

6  times  10  =  60 


7  times  10  =  70 


MULTIPLICATION 


8 

times 

2 

= 

16 

9 

times 

2 

= 

18 

8 

times 

3 

— 

24 

9 

times 

3 

= 

27 

8 

times 

4 

zrz 

32 

9 

times 

4 

= 

36 

8 

times 

5 

= 

40 

9 

times 

5 

= 

45 

8 

times 

6 

= 

48 

9 

times 

6 

=1 

54 

8 

times 

7 

= 

56 

9 

times 

7 

= 

63 

8 

times 

8 

= 

64 

9 

times 

8 

= 

72 

8 

times 

9 

=. 

72 

9 

times 

9 

= 

81 

8  times  10  =  80 


9  times  10  =  90 


11.  Because  of  the  large  number  of  business  transac- 
tions in  which  the  price  is  6J,  8J,  12^,  and  16§  cents  per 
article,  yard,  or  pound,  it  is  very  convenient  and  impor- 
tant to  memorize  a  merchant's  table  of  multiplication.  It 
is  as  follows : 


2 

times 

6J  = 

12* 

2 

times 

8£ 

= 

16J 

3 

times 

6£  = 

18f 

3 

times 

8* 

= 

25 

4 

times 

6i  = 

25 

4 

times 

8* 

sa 

33J 

5 

times 

6£  = 

3l£ 

5 

times 

8* 

= 

41f 

6 

times 

6i  = 

37* 

6 

times 

8* 

= 

50 

7 

times 

6J  = 

43| 

7 

times 

8* 

= 

58^ 

8 

times 

6J  = 

50 

8 

times 

8* 

±= 

66| 

9 

times 

6J  = 

56i 

9 

times 

8* 

= 

75 

10 

times 

6J  = 

62* 

10 

times 

8i 

= 

831 

2 

times 

12*  = 

25 

2 

times 

16f 

= 

33J 

3 

times 

12*  = 

37* 

3 

times 

ie§ 

= 

50 

4 

times 

12*  = 

50 

4 

times 

16| 

= 

66} 

5 

times 

12*  = 

62* 

5 

times 

16$ 

= 

83J 

6 

times 

12*  = 

75 

6 

times 

16$ 

= 

100 

7 

times 

12*  = 

87* 

7 

times 

16| 

= 

116f 

8 

times 

12*  = 

100 

8 

times 

16* 

= 

133^ 

9 

times 

12*  = 

112* 

9 

times 

16$ 

= 

150 

10 

times 

"1  0  1 

-*-  %  ~~~ 

125 

10 

times 

16§ 

= 

166§ 

10  FUNDAMENTAL  PEOCESSES 

EXERCISE 

1.  When  gingham  sells  at  8J$  per  yard,  what  will  be  the 
cost  of  5yd.?  7yd.?  9yd.?  4yd.?  10yd.? 

2.  When  lard  sells  at  16f$  per  pound,  what  will  be  the 
cost  of  3  lb.?  51b.?  91b.? 

3.  When  sugar  sells  at  6J$  per  pound,  what  will  be  the 
cost  of  8  lb.?  71b.?  61b.? 

4.  When  ribbon  sells  at  12^$  per  yard,  what  will  be  the 
cost  of  3yd.?  5yd.?  8yd.?  9yd.? 

12.  Memorize  the  following  table  of  important  equal  parts 
of  100 : 


«t=T5 

81  —  — 

"1O1     1                   OO  1     1 
2    —    8               OO-ir  —   -IT 

16§  =  J.         20     =  J 

25=  J 
50  =  £ 

13.  The  following  short  methods  of  multiplication  are 
useful. 

(1)  To  multiply  any  whole  number  by  10,  annex  a  cipher 
to  the  number ;  if  a  decimal  or  mixed  number  is  to  be  mul- 
tiplied by  10,  move  the  decimal  point  in  the  number  one 
place  to  the  right. 

EXAMPLE.  368  x  10  =  3680. 

37.56  x  10  =  375.6. 

ORAL    EXERCISE 

Name  rapidly  the  products  of  the  following  numbers 
when  multiplied  by  10 ;  by  100. 

1.  89.                 6.  285.  11.  87.5.  16.  8.57. 

2.  76.                  7.  8362.  12.  38.7.  17.  .26. 

3.  47.                  8.  9761.  13.  7.5.  18.  .07. 

4.  165.                9.  650.  14.  .6.  19.  .0387. 

5.  379.              10.  80.  15.  .16.  20.  1.02. 


DIVISION  11 

(2)  To  multiply  any  whole  number  by  33  J,  annex  two 
ciphers  to  the  number  and  divide  by  3. 

Since  33^  =  %  of  100,  to  annex  two  ciphers  to  any  num- 
ber and  divide  by  3  is  the  same  as  to  multiply  by  33^. 

EXAMPLE.  132  x  33J  =  13200  --  3  =  4400. 

EXERCISE 

1.  Show  that  to  multiply  1728  by  12^  is  the  same  as  to 
multiply  by  100  and  divide  by  8. 

2.  Show  that  to  multiply  364  by  25  is  the  same  as  to 
multiply  by  100  and  divide  by  4. 

3.  Show  that  to  multiply  1488  by  8J  is  the  same  as  to 
multiply  by  100  and  divide  by  12. 

4.  Show  that  to  multiply  1648  by  6J  is  the  same  as  to 
multiply  by  100  and  divide  by  16. 

5.  Multiply  936  by  8'  ;  by  12| ;  by  16§ ;  by  25  ;  by  33 J. 

DIVISION 

14.  The  following  short  methods  of  division  are  useful. 

(1)  To  divide  any  whole  number  by  10,  point  off  one 
decimal  place ;  if  a  decimal  or  mixed  number  is  to  be 
divided  by  10,  move  the  decimal  point  in  the  number  one 
place  to  the  left. 

EXAMPLE.  867  +-  10  =  86.7. 

36.5  -  10  =  3.65. 

ORAL   EXERCISE 

Name  rapidly  the  quotients  of  the  following  numbers 
when  divided  by  10;  by  100. 

1.  87.                 3.  273.  5.  638.  7.  1.6. 

2.  345.                4.  379.  6.  724.  8.  2780. 


12  FUNDAMENTAL  PROCESSES 

ORAL  EXERCISE 

Name  rapidly  the  quotients  of  the  following  numbers 
when  divided  by  10. 

1.  87.  5.  273.  9.  638.  13.  1.6. 

2.  345.  6.  379.  10.  724.  14.  2780. 

3.  75.  7.  274.  11.  3.7.  15.  8.9. 

4.  169.  8.  577.  12.  24.5.  16.  47.5. 

(2)  To  divide  any  whole  number  by  33J,  point  off  two 
decimal  places  and  multiply  by  3  ;  if  the  number  is  a  deci- 
mal or  mixed  number,  move  the  decimal  point  two  places 
to  the  left  and  multiply  by  3. 

Since  33^  =  ^  of  100,  to  move  the  decimal  point  two 
places  to  the  left  and  multiply  by  3  is  the  same  as  to  divide 
by  33|. 

EXAMPLE.  648  --  33£  =  6.48  x  3  =  19.44. 

(3)  To  divide  any  number  by  16§,  move  the  decimal 
point  in  the  number  two  places  to  the  left  and  multiply  by  6. 

Since  16§  =  £  of  100,  to  move  the  decimal  point  in  the 
number  two  places  to  the  left  and  multiply  by  6  is  the  same 
as  to  divide  by  16f  . 

EXAMPLE.  546  ~-  16  J  =  5.46  x  6  =  32.76. 

EXERCISE 

1.  Show  that  to  divide  484  by  25  is  the  same  as  pointing 
off  two  decimal  places  in  the  dividend  and  multiplying  by  4. 

2.  Explain  a  short  method  for  dividing  2567  by  50;  by 


3.  Divide  8976  by  33J  ;  by  12|  ;  by  16f  ;  by  25  ;  by  50. 


DECIMALS 

15.  Skill  in  the  use  of  decimals  in  everyday  life  depends 
mainly  upon  the  ability  to  multiply  and  divide  instantly 
by  10  or  some  power  of  10.  This  skill  may  be  acquired  by 
practice  exercises  in  multiplying  and  dividing  decimals  by 
10,  by  moving  the  decimal  point  one  place  to  the  right  when 
multiplying,  and  one  place  to  the  left  when  dividing.  Divi- 
sion may  be  indicated  by  the  sign  (-;-)  or  by  writing  the 
dividend  above  the  divisor  in  the  form  of  a  common  frac- 
tion ;  thus,  432  -j-  24,  or 


432 
'24   * 


ORAL   EXERCISE 

1.  Multiply  387.96  by  10;  by  100;  by  1000. 

2.  Multiply  .0167  by  10;  by  100;  by  1000. 

3.  Divide  379.4  by  10;  by  100. 

4.  Divide  753.21  by  10 ;  by  100 ;  by  1000. 

5.  Divide  .8  by  10;  by  100. 

6.  Divide  .25  by  10;  by  100. 

7.  Multiply  both  dividend  and  divisor  in  -    -  by  10. 

^4 

or»  rrcy 

8.  Multiply  both  dividend  and  divisor  in       '       by  10; 

by  100. 

1.728 

9.  Multiply  both  dividend  and  divisor  in  by  10; 

by  100. 

6  2575 

10.  Multiply  both  dividend  and  divisor  in    '          by  10; 

by  100 ;  by  1000. 

11.  State  the  effect  on  the  quotient  when  both  the  divi- 
dend and  the  divisor  are  multiplied  by  the  same  number. 

13 


14  DECIMALS 

16.  Division  of  decimals  is  made  easier  by  making  the 
divisor  a  whole  number. 

EXERCISE 

1.  $75-5-15  will  give  dollars  in  the  quotient.  How  many  ? 

2.  75  bu.  -T-  15  will  give  bushels  in  the  quotient.    How 
many  ? 

3.  75yd. -4-15  will   give   yards    in   the   quotient.    How 
many  ? 

4.  75  gal. -r- 15  will  give  gallons  in  the  quotient.    How 
many  ? 

5.  .75  -f-15  will  give  hundredths  in  the  quotient.    How 
many? 

6.  .075  -f-15  will  give  thousandths  in  the  quotient.    How 
many  ? 

7.  .0075 -f-15  will  give  ten-thousandths  in  the  quotient. 
How  many  ? 

The  divisor  is  an  abstract  and  whole  number,  and  the 
quotient  in  each  case  takes  its  name  from  the  dividend. 
Making  use  of  this  principle  in  the  division  of  decimals, 
always  make  the  divisor  a  whole  number  by  multiplying 
both  the  dividend  and  divisor  by  such  a  number  as  will 
make  the  divisor  a  whole  number. 

EXAMPLE.  .1875  ~  .25  =  .75. 

25)18.75(.75 
17  5 
125 
1  25 

The  divisor  is  made  an  integer  by  moving  the  decimal 
point  two  places  to  the  right  in  both  dividend  and  divisor. 
The  quotient  is  hundredths,  the  same  as  the  dividend. 


EXERCISE  15 

EXERCISE 
Divide : 

1.  10.36  by  .2.  6.  .0044  by  22. 

2.  .0032  by  .16.  7.  100  by  .01. 

3.  .0625  by  2.5.  8.  .01  by  20. 

4.  1728  by  .11.  9.  .2  by  200. 

5.  14.4  by  .36.  10.  .04  by  40. 

17.  The  term  "per  cent "  means  hundredths.    Hence, 
.12  =  12  per  cent.       .00}  =  }  per  cent. 

.07  =  7  per  cent.         1.25  =  125  per  cent. 
.09J  =  9J  per  cent.       .007  =  .7  of  a  hundredth  =  .7  per  cent 
The  sign  for  per  cent  is  %.    Therefore, 

.13=13%.  .00£=J%. 

1.69=169%.  .003  =  .3%. 

EXERCISE 

Express  the  following  by  using  the  per-cent  sign : 

1.  .18.         3.  .01.          5.  .006.         7.  .003.          9.  .OOJ, 

2.  .89.         4.  .OOJ.        6.  .0025.   .     8.  1.67.        10.  .001. 

18.  Any  number  written  as  a  per  cent  may  be  changed 
to  a  decimal  by  dropping  the  per-cent  sign  and  multiplying 
the  number  by  .01 ;  thus, 

27  %  =  27  x  .01  =  .27.  137  %  =  137  x  .01  =  1.37. 

.25%  =.25  x  .01  =.0025. 

EXERCISE 

Express  the  following  as  decimals  : 

1.  9%.  4.  .7%.  7.  1.9%. 

2.  8J%.  5.  .18%.    .  8.  2.25%. 

3.  139%.  6.  J%.  9.  8.3%. 


16  DECIMALS 

19.  Rule.   To  find  a  number  when  a  certain  number  of 
hundredth*  of  it  is  given,  divide  the  given  part  by  the  given 
hundredths. 

EXAMPLE.  56  is  .16  of  what  number  ? 

56  -  .16  =  350. 
Proof.  .16  of  350  =  56. 

EXERCISE 

1.  35  is  .12  of  what  number  ? 

2.  The  product  of  a  certain  number  multiplied  by  .24  is 
39.6.    What  is  the  number  ? 

3.  The  product  of  a  certain  number  multiplied  by  .17  is 
36.55.    What  is  the  number  ? 

4.  Multiply  75  by  .7.    The  product  must  be  divided  by 
what  number  to  give  75  as  quotient  ? 

5.  If  .16  of  a  hired  man's  monthly  wages  is  $4.80,  what 
are  his  wages  ? 

6.  If  $11.70  is  .14  of  the  wages  a  man  received  for 
3  mo.,  what  did  he  receive  ? 

7.  A  farmer  sold  280  head  of  cattle,  which  was  .35  of 
his  herd.    How  many  had  he  in  the  herd  ? 

8.  In  a  snowstorm  .2  of  a  flock  of  sheep  froze  to  death. 
If  13  died,  how  many  were  there  in  the  flock  ? 

9.  If   a   bank   loaned  .24   of   its    deposits,  which  was 
$10,400,  what  was  the  total  deposit  ? 

10.  If  10  A.  are  .8  of  a  potato  field,  how  many  acres  are 
there  in  the  field  ? 

20.  A  very  generally  used  method  of  computing  interest 
is  known  as  the  One  Dollar  Six  Per  Cent  Method.    The 
skillful  use  of  this  method  depends  upon  the  ability  to  take 
readily  a  fractional  part  of  a  decimal. 


EXEECISE  17 

21.  Rule.  To  take  a  fractional  part  of  a  decimal,  mul- 
tiply the  decimal  by  the  numerator  of  the  common  fraction 
and  divide  by  the  denominator. 

EXAMPLE.  Find  the  value  of  |  of  .041 J. 

.041  §  x  5  =  .208^, 
.208^-6  =  .034||. 

EXERCISE 


Find  : 

1. 

§ 

of 

.18. 

10. 

§ 

of 

.126. 

19. 

* 

of 

$.008. 

2. 

£ 

of 

.246. 

11. 

§ 

of 

.123. 

20. 

| 

of 

$.004. 

3. 

t 

of 

.8. 

12. 

I 

of 

.186. 

21. 

7 
S 

of 

$.002. 

4. 

J 

of 

.0111. 

13. 

* 

of 

.087. 

22. 

7 

of 

$.01£. 

5. 

i 

of 

.1. 

14. 

a 
1 

of 

.105. 

23. 

i 

of 

$.071. 

6. 

i 

of 

.01. 

15. 

7 

of 

.023. 

24. 

ft 

of 

$.031. 

7. 

§ 

of 

.01. 

16. 

\ 

of 

$.018J. 

25. 

5 

of 

$.18. 

8. 

§ 

of 

.OOJ. 

17. 

ft 
I 

of 

$.093^. 

26. 

7 

of 

$.241. 

9. 

§ 

of 

.135. 

18. 

fi 

of 

$.08j. 

27. 

£ 

of 

$.001. 

EDUCATION  AND  THRIFT 
EDUCATED  LABOR 

22.  A  business  man  who  has  studied  the  productive 
power  of  intelligent  labor  in  New  York  reports  that  the 
man  with  a  common-school  education  is  able  to  produce  one 
and  one-half  times  as  much  wealth  as  the  illiterate  man,  the 
high-school  man  two  times  as  much,  and  the  college  man 
four  times  as  much. 

EXERCISE 

1.  The  farm  hand  who  is  scarcely  able  to  read  and  write  is 
able  to  earn  $16  a  month.    If  he  had  a  common-school  educa- 
tion, how  much  more  should  he  earn  in  a  period  of  30  yr.? 

2.  If  a  laborer  who  signs  his  name  with  a  mark  is  able 
to  accumulate  $3000  in  20  yr.,  with  a  common-school  educa- 
tion how  much  more  should  he  have  accumulated  in  the 
same  time  ? 

3.  If  a  farmer  by  reading  farm  papers  and  books  on 
farming  30  min.  daily  for  a  year  can  grow  2  bu.  more  of 
grain  per  acre,  at  the  present  price  of  corn,  wheat,  and  oats 
how  much  does  he  profit  from  his  reading  in  growing  20  A. 
of  corn,  10  A.  of  oats,  and  20  A.  of  wheat  ?    Counting  10  hr. 
a  day's  work,  what  does  he  receive  for  a  day's  reading  ?    If 
this  is  50%  of  the  entire  gain  from  the  reading,  what  is  the 
total  for  a  year  ? 

4.  The  average  salary  of  the  man  who  has  completed  a 
college  course  is  about  $1000  per  year,  and  the  average  wages 
of  the  man  who  has  completed  the  common-school  studies 

18 


TRAINING  FOR  HEAD  AND  HAND  19 

are  about  $450.  What  will  be  the  difference  in  the  earnings 
of  the  two  men  at  the  end  of  a  work  period  of  40  yr.  ?  If  it 
takes  1440  days  to  complete  a  high-school  and  college  course, 
what  is  the  average  value  of  each  day  spent  in  taking 
such  a  course  ?  (The  college-trained  man  spends  8  yr.  of 
the  work  period  in  school  at  an  annual  expense  of  $250.) 
5.  Two  classmates  leave  the  country  school,  one  to  work 
for  75$  a  day  with  board ;  the  other  borrows  $250  and  goes 
away  3  yr.  to  a  trade  school  and  learns  a  trade  which  pays 
him  $1.75  a  day  with  board.  Counting  each  able  to  average 
285  work  days  a  year,  at  the  end  of  10  yr.  from  the  time 
they  leave  the  district  school  which  will  have  earned  the 
more  money? 

TRAINING  FOR  HEAD  AND  HAND 

23.  Manual  training  is  an  incentive  for  study.  The  pupil 
is  able  to  see  his  own  thoughts  given  expression  in  wood- 
work, and  thus  is  made  conscious  of  the  process  of  being 
educated.  The  result  is  more  personal  efficiency,  economy, 
and  a  higher  regard  for  education. 

EXERCISE 

1.  A  seventh-grade  boy  made  and  sold  in  his  first  36  one- 
hour  lessons  in  woodwork  the  following :  a  hatrack  for  $1, 
a  bookshelf  for  500,  a  checkerboard  for  25$,  two  picture 
frames  for  25$  each,  a  footstool  for  50$,  two  coat  hooks  for 
20$  each,  a  handkerchief  box  for  30$,  a  singletree  for  10$, 
and  two  hammer  handles  for  10$  each.    How  much  did  he 
earn  while  reciting  his  36  lessons  ? 

2.  A  boy  working  at  odd  times  during  a  school  term  of 
6  months  made  a  bookcase  for  which  he  received  $15.   How 
much  did  he  earn  each  month  besides  learning  geography, 
history,  grammar,  and  arithmetic  ? 


20 


EDUCATION  AND  THRIFT 


3.  Estimating  the  value  of  training  a  boy  how  to  handle 
and  care  for  tools  at  5$  for  each  work  day  he  lives,  what  is 
this  training  worth  to  a  man  in  the  course  of  40  yr.  ? 


INSTRUCTION  WHEN  TRANSMITTED  INTO  PERSONAL 
EFFICIENCY    MAKES  KNOWLEDGE   POWER 

4.  It  is  estimated  by  a  teacher  of  carpentry  that  the  boy 
without  training  in  the  use  of  tools  wastes  2  in.  on  the  length 
of  a  board  for  each  cut  he  makes  with  the  saw.    Estimate  the 
loss  on  100  cuts  of  6-inch  lumber  selling  at  $3  per  hundred. 

5.  If  a  boy  who  has  been  trained  in  the  use  of  tools  saves 
$15  a  year  in  the  repairs  and  convenient  articles  made  for 
the  home,  what  is  the  saving  in  50  yr.  ? 


IDLENESS  AND  CARELESSNESS  21 

IDLENESS,  CARELESSNESS,  AND  WASTE    OF 
MACHINERY 

24.  Idleness,  carelessness,  and  waste  of  machinery  can  be 
estimated  in  dollars.  Thus,  if  a  man  idles  away  a  day  when 
he  can  earn  $1.50  per  day  at  work,  he  has  lost  this  money 
as  completely  as  though  it  had  fallen  through  a  hole  in  his 
pocket. 


FARMING  WITHOUT  PROFITS 
EXERCISE 

1.  How  much  does  a  man  lose  who  idles  away  140  work 
days  each  year,  when  wages  are  75$  a  day  with  board  ? 

2.  In  a  family  of  5  children  of  school  age  only  one  attends 
school.    How  much  of  the  state's  school  fund  does  the  family 
lose  when  the  state  pays  $4.40  per  year  for  the  education  of 
each  child  ? 

3.  A  self-binder  that  cost  a  merchant  $100  was  left  out 
in  the  open  for  2  yr.  and  then  sold  for  $50.    Money  being 
worth  6%,  estimate  the  cost  of  this  carelessness. 


22 


EDUCATION  AND  THEIFT 


4.  A  farm  wagon  with  ordinary  usage,  and  kept  under 
shelter  when  not  in  use.  will  last  about  15  yr. ;  when  not 
sheltered  it  will  last  about  half  as  long.  What  is  the  average 
loss  per  year  on  a  $65  wagon  that  stands  out  in  the  open  ? 


KITCHEN  CABINET 

5 .  If  a  hired  hand  while  cultivating  young  corn  covers  up 
10  hills  to  the  acre,  what  is  the  value  of  the  corn  destroyed, 
counting  2  ears  to  the  hill  and  100  ears  to  the  bushel,  at  60<£ 
per  bushel  ? 

6.  If  the  hired  hand  in  problem  5  cultivates  3J  A.  per  day, 
what  is  the  actual  cost  to  the  farmer  for  a  day's  work  when 
the  man  is  paid  75$  per  day  ? 


PRODUCE,  GRAIN,  AND  STOCK  MARKET     23 

7.  Eead  in  some  good  book  for  30  min.  and  count  the 
words  read.    How  many  would  this  make  per  hour  ? 

8.  Calling  400  pages  with  400  words  to  the  page  an  aver- 
age-sized book,  how  many  good  books  could  you  read  each 
year  at  your  present  rate  of  reading  by  devoting  1  hr.  each 
day  to  them  ? 

9.  How  many  books  have  you  read  ?  Counting  400  pages 
to  the  book,  how  many  hours  have  you  spent  reading  good 
books  ? 

10.  A  kitchen  that  is  poorly  arranged  requires  the  mother 
to  take  100  more  steps  each  day  in  preparing  the  meals  than 
she  would  in  a  well-arranged  kitchen.    How  many  unneces- 
sary steps  does  she  take  in  a  year  ?    How  many  miles  is 
this?    (Allow  20  in.  to  a  step.) 

11.  If  a  kitchen  cabinet  saves  a  mother  50  twenty-inch 
steps  daily,  how  many  miles  is  she  saved  in  20  yr.  ? 

PRODUCE,  GRAIN,  AND  STOCK  MARKET 

25.  The  teacher  should  assist  and  encourage  his  pupils  to 
make  a  weekly  produce  and  grain  chart  of  the  local  and  city 
market  prices  of  all  the  farm  products  of  his  school  district. 
Any  good  daily  or  weekly  paper  will  give  the  city  market 
prices,  while  the  county  paper  will  give  the  local  or  home 
prices.  This  chart  should  be  tacked  on  the  wall  of  the  school- 
room, in  a  place  where  all  the  pupils  can  read  it.  Once  a 
week  a  new  one  should  be  made,  the  pupils  reporting  the 
market  prices. 

The  child  who  grows  up  to  be  a  farmer,  not  accustomed 
to  read  and  study  the  markets,  will  never  be  in  a  position 
to  command  the  highest  prices  for  his  products.  He  must 
know  the  markets  in  order  to  know  how  to  buy  and  sell 
intelligently. 


24 


EDUCATION  AND  THRIFT 

EXERCISE 


1.  Make  a  produce-,  grain-,  and  stock-market  chart  for  the 
week  beginning  September  8,  1913,  as  follows  : 


Name  of  article 


Local  market 
price 


City  market 
price 


Butter,  per  Ib 

Eggs,  per  doz 

Hens,  per  Ib 

Hogs,  per  cwt.     .    .    .  • . 
Steers,  fat,  per  cwt.     .    . 
Steers,  feeders,  per  c-wt. 
Yearlings,  per  cwt.       .    . 
Heifers,  per  cwt.      .    .    . 

Cows,  per  cwt 

Wheat,  per  bu 

Oats,  per  bu 

Corn,  per  bu 


2.  Find  the  amount  of  : 

3  doz.  eggs  @  180 

5  Ib.  butter  @  200 
10  Ib.  honey  @  12^0 

3.  Find  the  sum  due  a  person  who  sells : 

6  doz.  eggs  @  120 
30  Ib.  chickens  @  80 
35  Ib.  dried  fruit  @  4£0 


and  buys  : 


3  Ib.  coffee  @  200 

1  gal.  sirup  @  600 

2  gal.  oil  @  150 
8  Ib.  rice  @  60 

10  yd.  gingham  @  8^0 


POULTRY  PROBLEMS 
POULTRY  PROBLEMS 


25 


26.  The  Department  of  Agriculture  has  just  completed 
an  inquiry  into  the  causes  for  bad  and  addled  eggs.  It  re- 
ports that  farmers  could  save  several  million  dollars  a  year 
in  the  egg  industry  by  observing  the  following  rules :  give 


POULTRY  HOUSE  AND  CHICKENS 

the  hens  clean  nests ;  gather  the  eggs  at  least  once  daily ; 
keep  the  eggs  in  a  cool,  dry  place ;  market  the  eggs  at  least 
twice  a  week  ;  sell  all  mature  roosters  as  soon  as  the  hatching 
season  closes. 

EXERCISE 

1.  A  flock  of  30  hens  that  have  a  barnyard  for  a  run 
are  fed  daily  2  Ib.  of  wheat  worth  900  a  bushel.     If  the 
hens  average  80  eggs  a  year  each,  when  eggs  are  worth 
180  per  dozen,  what  is  the  profit  on  the  flock  ? 

2.  Keep  a  strict  account  of  the  feed  given  a  flock  of 
chickens  for  a  month  and  the  number  of  eggs  laid.    At  the 
local  price  of  feed  and  eggs,  determine  the  profit  or  the  loss 
on  the  flock  for  the  period. 


26  EDUCATION  AND  THEIFT 

3.  One  dozen  Barred  Plymouth  Eock  eggs  weighed  22  oz. 
and  one  dozen  Leghorn  eggs  weighed  16  oz.    How  many 
Leghorn  eggs  will  it  take  to  equal  in  weight  22  doz.  Barred 
Plymouth  Eock  eggs  ? 

4.  From  problem  3,  find  out  what  a  laboring  man  can 
afford  to  pay  per  dozen  for  Barred  Plymouth  Eock  eggs 
when  Leghorn  eggs  are  selling  at  11$  per  dozen.     Why 
should  eggs  be  sold  by  weight  ? 

5.  Capons  in  the  market  are  worth  more  than  hens.  What 
is  the  profit  on  36  capons  weighing  8  Ib.  each,  worth  8^-$ 
per  pound,  when  as  roosters  they  would  bring  only  4J$ 
per  pound  ? 

6.  What  is  the  difference  in  the  value  of  two  henu,  one 
laying  192  eggs  a  year  and  the  other  90  eggs  a  year,  if  the 
average  price  of  eggs  is  15$  per  dozen  ? 

7.  A  flock  of  50  hens  averages  93  eggs  a  year  each.    If 
the  average  price  of  eggs  is  15$  per  dozen,  what  is  the  value 
of  the  eggs  ? 

8.  If  it  takes  $15  worth  of  feed  to  keep  this  flock  for 
1  yr.,  what  is  the  profit  over  and  above  the  cost  of  feed  ? 

9.  A  poultry  journal  estimates  that  hens  on  the  farm 
average  80  eggs  a  year  each,  and  that  by  selecting  the  best 
layers  and  breeding  from  them,  an  average  of  135  eggs  a 
year  each  could  be  obtained.    What  would  this  difference 
amount  to  for  a  year  with  a  flock  of  75  hens,  when  eggs 
are  worth  16$  per  dozen  ? 

10.  The  Eastern  egg  buyers  have  discovered  by  years 
of  experience  that  one  out  of  every  five  eggs  coming  from 
a  certain  state  during  the  summer  is  bad,  and  they  make 
the  price  to  the  local  egg  buyers  accordingly.  When  the 
local  egg  buyer  pays  12$  per  dozen,  what  is  the  actual  value 
per  dozen  of  good  eggs  ?  What  is  the  loss  on  the  sale  of 
144  doz.  of  good  eggs  ? 


SPBAYING  27 

SPRAYING 

27.  Blight,  rot,  and  scab  are  fungous  diseases  of  orchards 
which  decrease  the  yield  and  quality  of  the  fruit  grown. 
Bordeaux  mixture  is  used  for  killing  fungous  growths,  such 
as  black  rot  and  scab  of  apples.    To  make  a  solution  for 
spraying,  dissolve  4  Ib.  of  freshly  slaked  lime  and  4  Ib.  of 
copper  sulphate  in  50  gal.  of  water.    If  chewing  insects  that 
destroy  plants  by  eating  the  leaves  are  also  to  be  destroyed, 
add  J  Ib.  of  Paris  green  or  3  Ib.  of  arsenate  of  lead  paste  to 
the  Bordeaux  mixture.    A  sufficient  amount  to  spray  one 
tree  is  2^-  gal. 

28.  A  Paris-green  solution,  consisting  of  £  Ib.  of  Paris 
green  mixed  with  50  gal.  of  water,  is  used  to  destroy  insects 
that  chew  the  leaves  of  potatoes. 

EXERCISE 

1.  In   the    spring   of   1910   the    Kentucky    Experiment 
Station  took  as  a  subject  for  demonstration  an  orchard  in 
Hardin  County  which  had  never  been  sprayed.    A  single 
row  of  trees  extending  through  the  orchard  was  sprayed 
twice  with  Bordeaux  mixture,  once  immediately  following 
the  blooming  period,  and  again  12  da.  later.    One  sprayed 
Maiden  Blush  tree  yielded  7  bu.  of  apples,  4J  bu.  of  which 
graded  "  firsts,"  the  remainder  "  seconds."    One  unsprayed 
tree  of  the  same  variety  in  the  next  row  yielded  4  bu.  of 
apples,   \  bu.   of  which   graded  firsts.    When  firsts  were 
selling  at  800  a  bushel  and  seconds  at  400,  what  was  the 
difference  in  the  market  value  of  the  fruit  grown  on  the 
two  trees  ? 

2.  When  the  yield  and  the  quality  of  the  fruit  in  the 
above  problem  is  an  average  for  sprayed  and  unsprayed 
trees,  what  will  be  the  difference  in  yield  in  two  orchards 


28  EDUCATION  AND  THRIFT 

of  150  trees  each,  one  sprayed  twice,  the  other  unsprayed  ? 
What  will  be  the  difference  in  their  value,  firsts  selling  at 
50$  per  bushel,  seconds  at  25$  per  bushel  ? 

3.  With  lime  at  1$  per  pound,  copper  sulphate  at  10$  per 
pound,  and  arsenate  of  lead  paste  at  20$  per  pound,  aver- 
aging 2  gal.  of  the  mixture  to  a  tree  for  a  single  spray,  what 
would  be  the  cost  of  spraying  100  apple  trees  twice  ? 

4.  If  the  orchard  in  problem  1  is  a  square  consisting 
of  10  A.,  with  the  trees  set  in  rows  30  ft.  apart  and  the  trees 
in  the  row  the  same  distance  apart,  what  would  be  the  cost 
of  the  material  for  spraying  the  orchard  twice  ?  What  would 
be  the  value  of  the  increased  yield  when  apples  of  the  first 
grade  sell  for  60$  per  bushel,  and  of  the  second  grade  for 
30$  per  bushel  ? 

5.  What  would  be  the  cost  of  the  material  required  to 
spray  an  orchard  of  50  trees  twice  ? 

6.  To  destroy  blight,  rot,  and  insects,  a  farmer  sprayed 
half  of  a  2-acre  field  of  potatoes  three  times  with  Bordeaux 
mixture  containing  Paris  green.  The  expense  was  as  follows : 
24  Ib.  of  lime  at  1^$  per  pound ;  24  Ib.  of  copper  sulphate  at 
24$  per  pound ;   1^  Ib.  of  Paris  green  at  30$  per  pound ; 
$4.25  for  labor.  The  sprayed  acre  yielded  165  bu.  of  potatoes, 
for  which  the  farmer  received  60$  per  bushel.   The  unsprayed 
acre  yielded  57  bu.,  for  which  he  received  60$  per  bushel. 
What  was  the  value  to  the  farmer  of  the  spraying  of  the 
1A.? 

7.  What  is  the  cost  of  materials  required  for  spraying  a 
10-acre  field  of  potatoes  three  times  for  insects,  if  Paris 
green  is  30$  a  pound  and  300  gal.  of  the  solution  are  used 
to  the  acre  ?    What  is  the  profit  for  spraying  if  the  labor 
cost  $22.50  and  the  increased  yield  is  worth  $75  ? 


VALUE  OF  BIRDS  TO  FARMERS  29 

THE  VALUE  OF  BIRDS  TO  FARMERS 

29.  Mr.  Beal,  of  the  United  States  Biological  Survey,  once 
estimated  that  the  tree  sparrow  in  a  single  season  in  the 
state  of  Iowa  ate  1,750,000  Ib.  of  weed  seed. 

Mr.  Chester  A.  Reed,  of  Massachusetts,  estimates  that  on 
an  average  each  bird  will  eat  daily  for  about  five  months  in 
the  year,  from  May  to  September  inclusive,  100  harmful 
insects.  He  also  estimates  120,000  insects  to  the  bushel. 

EXERCISE 

1.  If  15  Ib.  of  weed  seed  will  sow  1  A.,  how  many  acres 
of  weeds  would  the  seed  eaten  by  the  tree  sparrow  in  Iowa 
alone  have  sown  ?    At  650  an  acre  for  cutting,  raking,  and 
burning  the  weeds,  what  would  it  have  cost  the  farmers  of 
Iowa  to  destroy  the  weeds  ? 

2.  Counting  5  insect-eating  birds  to  the  acre,  how  many 
bushels  of  harmful  insects  will  the  birds  on  an  average-sized 
farm  in  your  community  destroy  during  5  mo.  ? 

3.  How  many  cutworms,  grubs,  and  harmful  insects  will 
be  destroyed  by  a  flock  of  50  birds  that  follow  the  plow 
daily  for  2wk.? 

4.  If  2  out  of  every  100  insects  and  worms  destroyed  are 
either  cutworms  or  grubs  (these  are  the  destroyers  of  young 
corn),  and  if  both  the  grubworm  and  the  cutworm  destroy 
on  an  average  3  corn  plants  daily,  what  is  the  value  of  the 
50  birds  following  the  plow  for  2  wk.,  when  corn  is  500  per 
bushel  ?  (Allow  one  good  ear  to  each  plant  destroyed.) 

5.  If  a  quail,  in  the  course  of  a  year,  eats  250  worth  of 
grain,  and  destroys  $2  worth  of  harmful  insects  and  weed 
seed,  how  much  has  a  farmer  injured  himself  by  killing 
3  pairs  of  quails  if  a  pair  raise  a  brood  of  12  each  year  ? 


PRACTICAL  MEASUREMENTS 
JUDGING  DISTANCE  AND  SURFACE 

30.  Every  one  should  be  so  familiar  with  the  units  of 
measure  that  he  can  measure  distance,  surface,  and  volume 
fairly  accurately  with  the  eye. 

EXERCISE 

1.  Lay  off  a  square  yard  on  the  wall  or  blackboard  with 
colored  crayon.    Put  it  in  a  conspicuous  place  and  do  not 
erase. 

2 .  In  one  corner  of  the  square  yard  lay  off  a  square  foot. 

3.  Make  an  estimate  of  the  number  of  square  yards  in 
the  schoolroom  floor ;  then  measure  and  determine  the  exact 
number. 

4.  Make  an  estimate  of  the  number  of  square  feet  in  the 
blackboard ;  then  measure  and  determine  the  exact  number. 

5.  How  many  square  feet  in  the  top  of  your  desk  ? 

6.  How  many  square  feet  in  the  floor  ? 

7 .  How  many  square  yards  in  the  wall  ? 

8.  Measure  a  rod  on  the  school  yard  and  mark  with  two 
firmly  set  stones  or  stakes. 

9.  Lay  off  300  ft.  by  accurate  measurement,  set  up  stakes 
at  each  end,  and  walk  this  distance  several  times,  counting 
the  number  of  steps  taken  each  time.    From  this  determine 
the  length  in  inches  of  your  average  step. 

10.  By  stepping,  estimate  a  quarter  of  a  mile. 

30 


LUMBER  MEASURE 
LUMBER  MEASURE 


31 


31.  A  board  foot  is  the  unit  in  measuring  lumber.  It 
is  a  board  1  ft.  square  and  1  in.  or  less  thick.  It  contains 
144  sq.  in. 

Lumber  dealers  usually  speak  of  board  feet  as  feet. 


EXERCISE 

1.  On  a  board  6  in.  wide,  mark  the  length  of  a  board  that 
will  contain  144  sq.  in.  (a  board  foot). 

2.  On  a  board  8  in.  wide,  mark  the  length  of  a  board 
that  will  contain  a 

board  foot. 

3.  On     a     board 
4  in.  wide,  mark  the 
length    of   a   board 
that  will  contain  a 
board  foot. 

4.  On     a     board 
10  in.    wide,    mark 
off  a  board  foot. 

32.  In  billing  lum- 
ber, the  number  of 
pieces  are  entered 
first,  then  the  thick- 
ness and  width  in 
inches,  then  the  length  in  feet.  In  recording  5  pieces,  6  in. 
thick  by  8  in.  wide  and  16  ft.  long,  the  form  would  be  thus, 
5  pc.  6"  x  8"  x  16'; 

and  would  be  read  off  by  a  lumberman,  "5  six-by-eight 
16  ft.77  Lumbermen  use  the  sign  (")  for  inches  and  (')  for 
feet,  instead  of  writing  inches  and  feet. 


3  Inches 


BOARD  MEASURE 


32  PEACTICAL  MEASUREMENTS 

33.  Rule.  To  find  the  number  of  board  feet  in  a  piece  of 
lumber,  divide  by  12  the  product  of  its  length  in  feet  by  its 
width  and  thickness  in  inches. 

The  work  may  usually  be  shortened  by  arranging  it  in 
the  form  for  cancellation.    Thus, 
3       4 


34.  Rule.  To  find  the  cost  of  a  bill  of  lumber,  divide  the 
number  of  board  feet  by  100  by  pointing  off  two  decimal 
places,  then  faultipty  by  the  price  per  hundred  feet. 

EXERCISE 

1.  Read  the  following  bill  of  lumber: 

23  pc.  4"  x    6"  x  12', 
7  pc.  4"  x    6"  x  16', 

15  pc.  2"  x    8"  x  20', 

16  pc.  2"  x    6"  x  20'. 

2.  Determine  the  number  of  board  feet  of  lumber  in 

10  pc.  2"x  4"X12', 

12  pc.  3"  x  8"  x  16', 

16  pc.  3"  x  6"  x  18', 

80  pc.  3"  x  8"  x  20'. 

3.  At  $1.75  per  hundred,  find  the  cost  of 

7  pc.  2"  x  10"  x  18', 
75  pc.  l"x  8"xl4', 
30pc.2"x  4"X12'. 

4.  Find  the  cost  of  the  following  : 

20  pc.  2"  x  4"  x  16'  at  $1.50  per  100, 

60  pc.  1"  x  6"  x  14'  at  $1.75  per  100, 

100  pc.  1"  x  4"  x  12'  at  $2.25  per  100. 


MEASURING  LUMBER  IN  THE  LOG          33 

5.  Determine  the  cost,  at  $1.75  per  hundred,  of  the  lumber 
required  to  build  a  yard  fence  168  ft.  long  and  6  boards  high, 
the  boards  used  being  12  ft.  long,  4  in.  wide,  and  1  in.  thick. 

6.  At  $2  per  hundred,  what  will  be  the  cost  of  the  lumber 
required  to  inclose  a  field  20  rd.  square  with  a  board  fence 
6  boards  high,  if  the  boards  are  10  ft.  long,  4  in.  wide,  and  1  in. 
thick  ? 

MEASURING  LUMBER  IN  THE  LOG 

35.  A  widely  used  rule  for  measuring  lumber  in  the  log 
is  the  following,  known  as  Doyle's  Rule : 

36.  Rule.    Subtract  4  in.  from  the  smallest  diameter,  -mul- 
tiply the  remainder  by  one  half  itself,  then  by  the  length  of 
the  Joe/  in  feet}  and  divide  by  8. 


LOG 


EXAMPLE.    How  many  feet  of  lumber  in  a  log  12  ft.  long  and  32  in. 
in  diameter  ?  73 


EXERCISE 

1.  Determine  the  number  of  board  feet  in  the  following: 
3  logs  14  ft.  long,  36  in.  in  diameter ;  2  logs  16  ft.  long, 
24  in.  in  diameter. 

2.  At  50$  per  hundred  for  sawing,  what  will  it  cost  to 
have  sawed  10  logs,  16  ft.  long  and  18  in.  in  diameter  ? 

3.  An  oak  tree  11  in.  in  diameter  contains  about  40  ft.  of 
lumber.    After  a  growth  of  8  yr.  it  contains  120  ft.    At  $1 


34-  PEACTICAL  MEASUREMENTS 

per  hundred,  what  is  the  value  of  the  growth  of  the  oak  in 
50  A.  of  forest,  averaging  30  oaks  to  the  acre  ? 

4.  A  poplar  tree  10  in.  in  diameter  contains  about  46  ft.  of 
lumber.   After  a  growth  of  10  yr.  it  contains  200  ft.   At  $1.75 
per  hundred,  what  is  the  value  of  the  growth  on  400  trees  ? 

5.  Estimating  one  railroad  tie  to  a  tree  11  in.  in  diameter, 
which  is  the  better  business :  to  cut  800  tie  trees  when  ties 
are  selling  at  55$  apiece,  delivered,  or  to  take  the  growth 
on  them  for  12  yr.,  at  which  time  the  trees  will  average 
170  ft.  and  will  be  'worth  $1.50  per  hundred  standing  ? 

6.  If  a  cubic  foot  of  oak  weighs  64  lb.,  what  is  the  weight 
upon  a  wagon  loaded  with  10  oak  ties  8  \  ft.  long,  9  in.  wide, 
and  7  in.  thick  ? 

7.  How  many  railroad  ties  9  in.  wide,  placed  15  in.  apart, 
are  required  for  1  mi.  of  track  ? 

CORDWOOD,  STOVE  WOOD,  AND  COAL 

37.  Cordwood  is  4  ft.  long.    A  cord  of  wood  is  a  pile  8  ft. 
long  and  4  ft.  high.    A  cord  of  stove  wood  is  a  pile  of  wood 
8  ft.  long,  4  ft.  high,  and  of  any  length  that  will  fit  a  stove. 

38.  Rule.    To  find  the  number  of  cords  of  wood  in  a  pile, 
multiply  the  length  of  the  pile  by  the  height  in  feet,  and 
divide  by  32. 

EXERCISE 

1.  If  a  cord  of  wood  for  cooking  purposes  lasts  a  family 
3  wk.,  how  much  does  the  family  pay  out  in  the  course  of  a 
year  for  cook-stove  wood  when  wood  is  $2  per  cord  ?   when 
wood  is  $3  per  cord  ? 

2.  How  many  cords  of  wood  are  there  in  a  pile  18  ft. 
long  and  4  ft.  high  ? 

3.  How  many  cords  of  oak  bark  are  there  in  a  pile  24  ft. 
long  and  10  ft.  high  ? 


CORDWOOD,  STOVE  WOOD,  AND  COAL       35 

4.  At  $6  per  cord,  what  is  the  value  of  a  pile  of  oak 
cordwood  40  ft.  long  and  6  ft.  high  ? 

5.  How  many  cords  of  wood  can  a  man  have  on  a  frame 
12  ft.  long  and  4  ft.  high  ? 

6.  Which  is  cheaper  for  a  man  living  in  town :  to  buy 
stove  wood  16  in.  long  at  $3  per  cord,  or  to  pay  $6  per  cord 


CORDWOOD 

for  cordwood  and  give  a  man  $2  to  saw  and  split  it  into 
stove  wood? 

7.  Is  it  cheaper  for  a  man  to  buy  stove  wood  16  in.  long 
at  $1.50  per  cord,  er  to  pay  $2  per  cord  for  cordwood  and 
give  a  man  $1.50  to  saw  and  split  it  into  stove  wood  ? 

8.  Make  an  estimate  of  the  number  of  cords  of  wood 
in  the  fallen  trees  that  are  wasting  on  your  father's  farm. 
What  is  the  value  of  this  wood  at  $2  per  cord  ? 

9.  How  many  cords  of  wood  16  in.  long  can  be  placed  cross- 
wise in  a  wagon  bed  10  ft.  long,  3  ft.  wide,  and  14  in.  deep  ? 

10.  How  long  must  a  pile  of  wood  10  ft.  high  be  to  con- 
tain 18  cords  ? 

39.  One  ton  contains  35  cu.  ft.  of  hard  coal. 


36  PRACTICAL  MEASUREMENTS 

EXERCISE 

1.  How  many  bushels  of  coal  are  there  in  a  wagon  bed 
9  ft.  long,  3  ft.  wide,  and  15  in.  deep  ? 

2.  How  many  tons  of  coal  will  a  coal  shed  12  ft.  long, 
8  ft.  wide,  and  7  ft.  high  hold  ? 

3.  Measure  the  thickness  of  a  vein  of  coal  in  your  neigh- 
borhood and  estimate  the  number  of  tons  under  an  acre  of 
land.    What  is  it  worth  at  10$  per  ton  ? 

4.  How  many  tons  of  coal  can  be  placed  in  a  car  36  ft 
long,  8  ft.  wide,  and  5  ft.  deep  ? 

LIQUID  MEASURE 

40.  The  liquid  gallon  contains  231  cu.  in.  and  the  barrel 
3l£  gal.  A  cubic  foot  contains  1728  cu.  in.  For  practical 
purposes  count  7£  gal.  to  every  cubic  foot  of  water. 

EXERCISE 

1.  Make  a  box  whose  inside  measurements  are  11  in.  by 
7  in.  by  3  in.    Fill  the  box  level  full  of  sand,  then  pour  the 
sand  into  a  bucket  and  mark  its  depth.    This  may  be  used 
as  a  gallon  measure. 

2.  Using  your  marked  bucket  as  a  measure,  find   the 
capacity  of  several  different  vessels. 

3.  Saw  a  1-inch  cube  from  a  board  1  in.  thick. 

4.  Saw  a  square  foot  from  a  board   1  in.  thick.    What 
must  be  the  width  of  the  board  ?    How  many  1-inch  cubes 
does  it  contain  ? 

5.  Make  a  box  whose  inside  measurements  are  12  in.  by 
12  in.  by  12  in.    How  many  1-inch  cubes  does  it  contain  ? 


SPECIFIC  GRAVITY  37 

6.  How  many  gallons  of  milk  can  be  put  into  a  can 
containing  1386  cu.  in.  ? 

7.  How  many  gallons  of  water  are  there  in  a  well  4  ft. 
in  diameter,  when  the  water  stands  6  ft.  deep  ? 

SUGGESTION.  For  practical  purposes,  square  one  half  the  diameter 
in  feet,  multiply  by  3|,  by  the  depth  in  feet,  and  by  7^. 

8.  How  many  barrels  of  water  are  there  in  the  well  in 
problem  7  ? 

9.  How  many  gallons  of  water  are  there  in  a  well  6  in. 
in  diameter,  when  the  water  stands  10  ft.  deep  ? 

10.  How  many  gallons    of  water  will  a  tank   6  ft.  in 
diameter  and  2  ft.  deep  hold  ? 

11.  How  many  gallons  of  water  will  a  barrel  contain,  the 
head  diameter  being  20  in.,  the  bung  diameter  24  in.,  and 
the  length  30  in.  ? 

20  in.  -f  24  in. 
SUGGESTION.   -      — - —     —  =  22  in.,  the  average  diameter. 

12.  Measure  a  cistern  and  approximate  the  number  of 
gallons  it  will  contain. 

13.  How  many  gallons  will  a  bucket  contain,  the  head 
diameter  being  10  in.,  the  bottom  diameter  9  in.,  and  the 
depth  10  in.  ? 

SPECIFIC  GRAVITY 

41.  The   specific  gravity  of   a   substance   is   its  weight 
measured  by  the  weight  of  an  equal  volume  of  pure  water. 

Any  substance  whose  weight  is  less  than  the  weight  of 
an  equal  volume  of  water  will  float.  One  cubic  foot  of 
water  weighs  62.5  Ib. 

42.  Weigh  a  pailful  of  sand  very  carefully  and  subtract 
the  weight  of  the  pail.    Then  weigh  a  pailful  of  water  and 


38  PRACTICAL  MEASUREMENTS 

subtract  the  weight  of  the  pail.  Now  divide  the  weight  of 
the  sand  by  the  weight  of  the  water.  The  quotient  is  called 
the  specific  gravity. 

If  the  substance  whose  specific  gravity  is  to  be  found  is 
of  an  irregular  shape,  —  for  instance,  a  piece  of  iron, — 
weigh  it.  Then  place  it  in  a  pailful  of  water.  Some  of 
the  water,  an  amount  equal  to  the  bulk  of  the  substance, 
will  run  out.  Weigh  the  water  that  runs  out,  and  divide 
the  weight  of  the  substance  by  the  weight  of  the  water 
that  runs  out.  The  quotient  will  be  the  specific  gravity 
of  the  substance. 

43.  Rule.   To  find  the  specific  gravity  of  a  substance,  divide 
its  weight  by  the  weight  of  an  equal  volume  of  water. 

EXERCISE 

1.  A  cubic  foot  of  zinc  weighs   437.5  lb.,  and  a  cubic 
foot  of  water  weighs  62.5  lb.    What  is  the  specific  gravity 
of  the  zinc  ? 

2.  A  cubic  foot  of  lead  weighs  712.5  lb.,  and  a  cubic 
foot  of  water,   62.5  lb.     What   is   the  specific  gravity  of 
the  lead? 

3.  The  specific  gravity  of  cast  iron  is  7.4.    What  is  the 
weight  of  a  bar  2  ft.  long,  9  in.  wide,  and  8  in.  thick  ? 

4.  Find  the  specific  gravity  of  a  pailful  of  gravel,  and 
estimate  the  weight  of  a  load  of  gravel  in  a  bed  9  ft.  long, 
3  ft.  wide,  and  12  in.  deep. 

5.  A  flatboat  40  ft.  long  and  12  ft.  wide  sinks  2^-  in.  when 
a  team  drawing  a  load  of  wheat  is  driven  upon  it.   What 
is  the  combined  weight  of  the  team,  wagon,  and  load .? 

6.  To  what  depth  will  400  bu.  of  wheat  sink  a  flatboat 
60  ft.  long  and  18  ft.  wide  ? 


LAND  MEASURE 


39 


7.  The  specific  gravity  of  oak  is  .75,  of  poplar  .45,  of 
white  pine  .4.   Compare  the  weights  of  a  sill  of  each  12  ft. 
long,  12  in.  wide,  and  10  in.  thick. 

8.  If  a  cubic  foot  of  water  weighs  62.5  lb.,  and  the  specific 
gravity  of  ice  is  .92,  what  is  the  weight  of  a  cubic  foot  of  ice  ? 

9.  If  a  gallon  of  water  weighs  8.35  lb.,  and  the  specific 
gravity  of  milk  is  1.03,  what  is  the  weight  of  a  gallon  of 
milk? 

10.  If  a  gallon  of  water  weighs  8.35  lb.,  and  the  specific 
gravity  of  oil  is  .9,  what  is  the  weight  of  the  oil  in  a  barrel 
holding  40  gal.  ? 

LAND  MEASURE 

44.  A  rectangular  field  is  one  bounded  by  four  straight 
lines,  having  four  square  corners.  An  acre  contains  160  sq.  rd. 

EXERCISE 

1.  Lay  off  a  square  rod  on  the  school  yard,  and  mark 
with  4  firmly  set  stakes. 

2.  Lay    off    an    acre    of   land   in   the   form   of  a   rec- 
tangle  near   your   schoolhouse,   and   mark   with   stakes. 


Area  =  Length  rimes  width 


Length 


RECTANGULAR  FIGURE 

3.  How  many  acres  are  there  in  a  rectangular  field  80  rd. 
long  by  60  rd.  wide  ? 

4.  What  must  be  the  width  of  a  rectangular  field  80  rd. 
long  to  contain  25  A.  ? 


40 


PEACTICAL  MEASUREMENTS 


TRIANGULAR  DIAGRAM 


45.  A  triangular  field  is  one  bounded  by  three  straight  lines. 

The  altitude  of  a  triangle 
is  the  perpendicular  distance 
between  the  base  of  the  tri- 
angle and  the  highest  point 
opposite  it. 

Lines  are  perpendicular  (J_) 
to  each  other  when  they  meet 
forming  a  square  corner. 

If  two  sides  of  a  triangle  are 
perpendicular  to  each  other, 
the  triangle  is  called  a  right 
triangle. 

EXERCISE 

1.  Cut  a  4-inch  square  into  2  equal  right  triangles.    How 
many  square  inches  are  there  in  each  triangle  ?   At  a  point 
halfway  between  the  base  and 

the  apex  of  one  of  the  trian- 
gles, cut  on  a  line  parallel  with 
the  base,  and  so  place  the  two 
parts  as  to  form  a  rectangle. 
Now  make  your  own  tule  for 
measuring  a  triangle. 

2.  How  many  acres  are  there 
in  a  triangular  field  the  longest 
side   of  which  is  30  rd.,  and 
the  altitude  of  which  from  the 
opposite  corner  to  this  side  is 
35  rd.? 

3.  Stake  off  a  small  trian- 
gular field,  measure  the  longest  side  and  the  altitude  from 
the  corner  opposite  this  side,  and  determine  the  number  of 
acres. 


DIAGRAM  ILLUSTRATING 

RULE  FOR  FINDING  AREA 

OF  A  TRIANGLE 


LAND  MEASUEE 


41 


4.  Select  a  triangular  field  near  the  schoolhouse,  measure 
it,  and  estimate  the  number  of  acres  it  contains. 

5.  A  farmer  has  2  rectangular  pieces  of  land  to  fence; 
one  is  40  rd.   by  40  rd.,  the  other  80  rd.  by  20  rd.    How 
much  will  it  cost  to  fence  each  at  55$  per  rod  ?   How  many 
acres  in  each  field  ? 

6.  Select    an    irregular 
4-sided     field     near     the 
schoolhouse,  and  estimate 
the    number    of    acres    it 
contains. 

NOTE.  To  measure  the  acres 
in  an  irregular,  4-sided  field, 
measure  the  diagonal  (the  dis- 
tance from  one  corner  to  the 
opposite  corner),  and  solve  each 
triangle.  Their  sum  will  be  the 
area  of  the  field. 


FOUR-SIDED  FIELD 


46.  Barbed  wire  is  sold 
by  the  roll.    The  average- 
sized  roll  weighs  100  Ib.   One  pound  of  barbed  wire  averages 
12  ft.  in  length.    A  pound  of  staples  contains  about  100. 


EXERCISE 

1.  How  many  rolls  of  wire  and  pounds  of  staples  must 
be  bought  for  80  rd.  of  fence  3  wires  high,  the  posts  being 
12  ft.  apart  ? 

2.  With  wire  at  $1.75  per  cwt.,  and  staples  at  40  per 
pound,  estimate  the  cost  of  the  wire  and  staples  required  to 
build  f  mi.  of  fence  4  wires  high. 

3.  A  fence   80  rd.  long  is  built  out  of  posts  set  12  ft. 
apart  with  woven  wire  27  in.  high,  and  3  strings  of  barbed 


42  PRACTICAL  MEASUREMENTS 

wire.  What  is  the  cost  of  the  fence  when  posts  cost  15$ 
each,  woven  wire  23$  per  rod,  and  barbed  wire  1.8$  per  rod? 
4.  A  fence  answering  the  same  purpose  could  have  been 
built  with  the  same  number  of  posts  at  the  same  price,  using 
woven  wire  48  in.  high  at  27$  per  rod.  What  would  have 
been  the  difference  in  the  cost  of  the  two  fences  ? 

AREAS  OF  STATES 

47.  Maps  are  drawn  to  a  scale,  that  is,  1  in.  on  a  map 
may  be  used  to  represent  80,  90,  or  100  mi.,  etc.    From 
the  scale  of  a  map  the  area  of   the   surface   represented 
may  be  determined. 

48.  Rule.   To  determine  approximately  the  area  of  a  state 
or  a  county  from  a  map  drawn  to  a  scale,  square  the  number 
represented  by  1  in.  on  the  scale  and  multiply  the  product  by 
the  number  of  square  inches  in  the  map.    The  result  will  be 
the  area  in  square  miles.    If  the  state  is  irregular  in  shape, 
use  an  average  length  and  width. 

EXERCISE 

1.  A  square  surface  4  ft.  long  is  represented  by  a  drawing 
1  ft.  square.    In  what  ratio  are  the  dimensions  diminished  ? 
The  surface  of  the  drawing  (1  sq.  ft.)  represents  how  many 
square  feet  of  the  original  surface  ? 

2.  A  square  surface  3  ft.  long  is  represented  by  a  draw- 
ing 1  ft.  square.    In  what  ratio  are  the  dimensions  dimin- 
ished?   The  surface  of  the  drawing  represents  how  many 
square  feet  of  the  original  surface  ? 

3.  A  rectangular  surface  12  in.  by  8  in.  is  represented  by 
a  drawing  3  in.  by  2  in.    In  what  ratio  are  the  dimensions 
diminished  ?    How  many  square  inches  of  the  original  sur- 
face does  1  sq.  in.  of  the  drawing  represent  ? 


PAPERING  43 

4.  Colorado  is  represented  on  a  map  as  3  in.  long  and 
2£  in.  wide.    The  scale  of  the  map  is  1  in.  for  every  124  mi. 
Find  the  approximate  area  of  the  state. 

5.  Consult  a  map  of  North  Dakota  and  determine  the 
area  of  the  state. 

6.  Kansas  is  represented  on  a  map  as  4.125  in.  long  and 
2.625  in.  wide.   The  scale  of  the  map  is  1  in.  for  every  97  mi. 
Find  the  approximate  area  of  the  state. 

7.  If  .05  in.  on  a  certain  map  represents  a  mile,  what  is 
the  scale  of  the  map  ? 

8.  If  .06  in.  on  a  map  represents  1.8  mi.,  what  is  the  dis- 
tance on  the  map  between  two  places  if  their  real  distance 
apart  is  75  mi.  ? 

PAPERING 

49.  Rule.  To  estimate  the  number  of  rolls  of  paper  re- 
quired for  the  ivalls  of  a  room,  multiply  the  distance  around 
the  room  in  feet  by  the  height  in  feet  and  divide  by  72  if  the 
rolls  are  double,  and  by  36  if  the  rolls  are  single.  Deduct  a 
double  roll  for  each  three  openings. 

A  fractional  roll  is  counted  as  a  whole  roll. 

EXERCISE 

1.  How  many  double  rolls  of  paper  would  it  take  to  paper 
the  walls  of  your  schoolroom  ?  the  ceiling  ? 

2.  At  15$  per  double  roll  for  walls  and  ceiling,  and  15$  per 
roll  for  border,  what  would  the  paper  for  the  schoolhouse  cost? 

3.  At  20$  per  double  roll  for  walls  and  ceiling,  and  20$ 
per  double  roll  for  border,  what  would  the  paper  cost  for 
your  living  room  at  home  ? 

4.  How  much  would  it  cost  to  paper  your  dining  room 
with  paper  at  18$  per  double  roll,  the  border  at  the  same 
price,  and  20$  per  double  roll  the  price  for  hanging  ? 


44  PEACTICAL  MEASUREMENTS 

CARPETING 

50.  Carpeting  is  usually  f  yd.  or  1  yd.  wide,  and  matting 
is  1  yd.  wide.    They  are  sold  by  the  yard.    The  number  of 
yards  needed  for  a  given  room  depends  upon  the  way  the 
strips  are  to  run  —  that  is,  lengthwise  or  across  the  room  — 
and  the  amount  of  waste  in  matching.    A  fractional  part  of 
a  strip  cannot  be  bought. 

51.  Rule.   To  determine  the  number  of  yards  required  to 
carpet  a  roomy  decide  which  way  the  strips  shall  run,  and 
estimate  their  length  and  number.    Add  to  the  length  of  each 
strip  after  the  first  the  allowance  for  waste  in  matching.    The 
combined  length  of  the  strips  in  feet  divided  by  3  will  give 
the  number  of  yards  required. 

EXERCISE 

1.  Measure  your  schoolroom  floor   and  determine  how 
many  yards  of  matting  it  would  take  to  cover  it,  placing 
the  strips  lengthwise  ;  crosswise. 

2.  Bring  to  school  the  dimensions  of  your  living  room, 
and  estimate  the  most  economical  way  of  covering  the  floor 
with  matting  worth  35$  per  yard. 

3.  A  room  13^  ft.  by  10  ft.  is  to  be  carpeted  with  carpet 

1  yd.  wide  at  80$  per  yard.    Which  is  the  more  economical 
way  of  laying  the  strips  ?   How  much  more  economical  is  it  ? 

4.  Find  the  cost  of  carpeting  a  room  16  ft.  6  in.  by  12  ft. 

2  in.  with  carpeting  f  yd.  wide  at  $1.10  per  yard,  when  the 
strips  are  laid  lengthwise.    Allow  for  a  waste  of  9  in.  on 
each  .strip  in  matching  the  pattern. 


CONSERVATION  OF  THE  SOIL 

SOIL  EROSION      ' 

52.  Soil  erosion  is  the  washing  away  of  the  soil  by  rain  and 
snow.  It  is  prevented  by  proper  crop  rotation  and  by  keeping 
all  ditches  filled  with  rock  or  brush  or  some  other  substance. 


ERODED  FIELD 
EXERCISE 

1.  Ordinary  sandstone  will  hold  -1-  of  its  bulk  of  water. 
How  many  gallons  of  water  are  there  in  a  bed  of  sandstone 
underlying  a  5-acre  field,  if  it  is  10  ft.  thick  and  soaked 
with  water  ? 

45 


46 


CONSERVATION  OF  THE  SOIL 


2.  After  a  heavy  summer  rain  the  water  of  a  small  stream 
contained  1  Ib.  of  sediment  for  every  500  gal.  of  water.    If 
the  rainfall  was  1  in.,  the  area  of  the  basin  drained  4  sq.  mi., 
and  the  amount  of  water  that  ran  off  1  of  all  that  fell,  how 
much  soil  did  the  rain  carry  away  ? 

3.  After  a  heavy  rain  the  water  of  a  small  stream  that 
drained  a  meadow  contained  1  Ib.   of  sediment  for  every 
2000  gal.  of  water.    If  the  rainfall  was  2  in.,  and  1  of  all  the 
water  that  fell  ran  off,  how  much  soil  was  carried  away  from 
a  40-acre  meadow  ? 

4.  If  the  water  running  from  a  piece  of  land  that  has 
been  planted  with  corn  contained  1  Ib.   of   sediment  for 
every  250  gal.  of  water,  how  much  soil  was  carried  away 
from  a  40-acre  cornfield  after  a  2-inch  rainfall,  J  of  the 
water  running  off  ? 


TAX  UPON  THE  SOIL  BY  DIFFERENT  CROPS 

53.  Nitrogen,  phosphoric  acid,  and  potash  are  the  most 
important  plant  foods  contained  in  the  soil.    They  are  ex- 
tracted from  the  soil  in  different  proportions  by  different 
crops.    Clover,  cowpeas,  and  a  few  other  crops  draw  their 
nitrogen  from  the  air  and  thus  save  the  soil. 

54.  The  table  below  will  give  some  idea  of  the  amount  of 
plant  food  removed  from  the  soil  in  growing  certain  crops. 


Crops 

Straw 

Grain 

Nitrogen 

Phosplioric 
acid 

Potash 

Pounds 

Bushels 

Pounds 

Pounds 

Pounds 

Corn  .    .    . 

3000 

50 

74 

26 

42 

Wheat    .    . 

2000 

20 

38 

15 

23 

Oats  .    .    . 

2500 

50 

48 

18 

40 

Clover    .    . 

2000 

11 

36 

Cowpeas     . 
Timothy  hay 

2000 
2000 

24 

10 
10 

40 
18 

THE  COST  OF  RESTORING  PLANT  FOOD     47 

EXERCISE 

1.  How  many  pounds  of  plant  food  are  required  to  grow 
18  A.  of  corn,  averaging  50  bu.  to  the  acre  ? 

2.  How  many  pounds  of  plant  food  are  required  to  grow 
18  A.  of  clover,  averaging  2  tons  to  the  acre  ?    averaging 
1  ton  to  the  acre  ? 

3.  What  is  the  tax  upon  the  soil  in  growing  a  50-acre 
field  of  wheat,  averaging  20  bu.  to  the  acre  ? 

4.  What  is  the  value  of  the  plant  food  removed  from  the 
soil  in  growing  50  bu.  of  corn,  nitrogen  being  quoted  in  the 
market  at  22$  a  pound,  phosphoric  acid  at  5$  a  pound,  and 
potash  at  6$  -a  pound  ? 

5.  A  father  tells  his  son  that  he  may  have  all  the  wheat 
he  can  grow  on  a  10-acre  field  if  he  will  pay,  at  commercial 
prices  (see  problem  4),  for  the  plant  food  removed  from  the 
soil.    If  the  son  grows  20  bu.  per  acre,  how  much  does  he 
owe  his  father  ? 

THE  COST  OF  RESTORING  PLANT  FOOD  TO 
THE  SOIL 

55.  Nitrogen,  phosphoric  acid,  and  potash  may  be  re- 
turned to  the  soil  by  means  of  commercial  fertilizer,  straw, 
and  manures. 

56.  The  table  on  the  following  page  gives  some  idea  of 
how  plant  food  may  be  returned  to  the  soil,  and  what  it 
is  worth  per  ton  at  commercial  prices :  nitrogen,  20$  per 
pound ;  potash,  5$ ;  and  phosphoric  acid,  5$. 

Pupils  should  complete  the  table  with  values  based  on 
commercial  prices,  and  make  a  duplicate  copy  on  a  large 
piece  of  pasteboard  for  their  parents  to  inspect  and  to  keep 
for  future  reference. 


48 


CONSERVATION  OF  THE  SOIL 


POUNDS  PER  TON 

MARKET  VALUE  PER  TON 

NAME  OF  MATERIAL 

Nitro- 
gen 

Phos- 
phoric 
acid 

Potash 

Nitro- 
gen 

Phos- 
phoric 
acid 

Potash 

Total 
value 

Fresh  farm  manure   . 

10 

5 

10 

$2.00 

$0.25 

$0.50 

$2.75 

Barnyard  manure 

10 

5 

10 

Corn  stover,   .... 

20 

6 

28 

Oat  straw  

12 

4 

24 

Wheat  straw.    .    .    . 

12 

2 

10 

Clover  hay     .... 

41 

7 

44 

Cowpeas    

39 

10 

29 

Rye  straw      .... 

9 

5 

16 

Redtop  

23 

7 

20 

Average,  complete    . 

Commercial  fertilizer 

33 

33 

33 

EXERCISE 

1.  What  is  the  loss  in  plant  food  to  a  farmer  who  burns 
a  straw  stack  weighing  20  tons  ? 

2.  How  much  plant  food  does  a  farmer  lose  when  selling 
the  fodder  from  a  10-acre  field  averaging  50  bu.  per  acre  ? 

3.  What  is  the  value  of  the  plant  food  returned  to  the 
soil  when  25  A.  of  clover,  averaging  1  ton  per  acre,  are 
plowed  under  ? 

4.  How  does  the  value  of  1  ton  of  fresh  farm  manure 
compare  with  that  of  1  ton  of  cowpeas  plowed  under  for  fer- 
tilizer ?    (A  ton  of  fresh  manure  shrinks  one  half  in  weight 
during  the  first  six  months  when  exposed  to  the  weather.) 

5.  How  does  1  ton  of  barnyard  manure  compare  in  soil 
fertility  with  1  ton  of  wheat  straw  ? 

6.  What  is  the  loss  on  10  tons  of  piled  manure  exposed 
6  or  more  months  ?   (Make  an  estimate  based  on  the  com- 
mercial value  of  plant  food  given  in  the  table.") 


COMPAEATIVE  VALUE  OF  MANURES        49 

7.  What  is  the  value  of  the  plant  food  in  the  cornstalks 
from  1  A.,  when  the  stalks  weigh  3500  Ib.  ? 

8.  It  is  estimated  that  a  1000-pound  steer  during  the 
process  of  fattening  makes  .9  ton  of  manure  per  month. 
What  is  the  value  of  the  manure  from  a  herd  of  20  for 
3  mo.  ? 

9.  It  is  estimated  that  the  value  of  the  manure  produced 
annually  by  a  farm  horse  is  $30 ;  that  produced  by  the  cow, 


BARN  WHERE  THE  MANURE  IS  WASHED  AWAY 

$24 ;  and  that  produced  by  the  hog,  $10.  If  the  statement 
is  true  that  the  average  farmer  saves  only  ^  of  the  value  of 
the  manure  on  the  farm,  what  is  the  annual  loss  on  2  horses, 
3  cows,  and  5  hogs  ? 


THE  COMPARATIVE  VALUE  OF  MANURES 

57.  The  table  on  the  following  page  gives  the  analysis  of 
farmyard  manures  made  by  the  Department  of  Agriculture 
at  Washington,  D.C. 

58.  When  nitrogen  is  worth  20$  per  pound,  potash  6$, 
and  phosphoric  acid  5$,  complete  the  table  by  estimating 
the  value  of  each  ton  of  manure. 


50 


CONSERVATION  OF  THE  SOIL 


Manure 
water 

Nitrogen 

Phosphoric 
acid 

Potash 

Value  per 
ton 

Cattle  .    .    . 

75.25% 

.426% 

.29% 

.44% 

Horse   .    .    . 

48.69% 

.49% 

.26% 

.48% 

Hog.    ... 

74.13% 

.84% 

.39% 

.32% 

Sheep   .    .    . 

59.52% 

.768% 

.391% 

.591% 

Chicken    .    . 

56% 

.8% 

.5% 

.85% 

EXERCISE 

1.  The  Maryland  Agricultural  Experiment  Station  grew 
65.1  bu.  of  corn  on  land  which  had  been  given  one  applica- 
tion of  rotted  manure ;  on  adjoining  land  it  grew  70.7  bu. 
of  corn  from  an  equal  amount  of  fresh  manure.    What  was 
the  per  cent  of  gain  from  using  fresh  manure  ? 

2.  At  the  same  station  fresh  manure  when  used  as  a  top- 
dressing,  instead  of  being  plowed  under,  resulted  in  a  gain 
of  10  bu.  of  corn  per  acre.    The  yield  of  corn  on  the  land 
where  the  manure  was  plowed  under  was  87  bu. ;  what  was 
it  on  the  other  ?    What  was  the  per  cent  of  gain  from  using 
the  manure  as  a  top-dressing  ? 

3.  On  an  unman ured  piece  of  land  16  bu.  of  wheat  was 
the  average  yield  per  acre.    The  same  land  when  given  a 
top-dressing  of  fresh  manure   made  an  average  yield   of 
20  bu.    What  was  the  per  cent  of  increase  of  the  manured 
land  over  the  umnanured  ? 

MIXING  FERTILIZERS  ON  THE  FARM 

59.  It  is  usually  much  cheaper  and  more  satisfactory  to 
buy  the  fertilizer  ingredients  and  mix  them  on  the  farm.  A 
fertilizer  labeled  2-8-4  contains  2%  nitrogen,  8%  phos- 
phoric acid,  and  4%  potash.  (In  some  states  the  order  of 
naming  the  ingredients  is  phosphoric  acid,  nitrogen,  and 
potash.) 


MIXING  FERTILIZERS  ON  THE  FAKM       51 

60.  Commercial  fertilizers  are  used  for  the  nitrogen,  phos- 
phoric acid,  and  potash  they  contain.   Nitrogen  is  obtained 
chiefly  from  nitrate  of  soda,  dried  blood,  dried  fish  scrap, 
and  cottonseed  meal.    Phosphoric  acid   is    obtained  from 
ground  bone,  basic  slag,  ground  phosphate  rock,  and  acid 
phosphate.    Potash   is    obtained  from   muriate  of  potash, 
sulphate*  of  potash,  and  kainite. 

61.  Fertilizer  materials  are  about  as  follows  :    Chilean 
nitrate  of  soda,  15%  ;  acid  phosphate,  16%  ;  and  muriate 
of  potash,  50%. 

The  prices  of  these  materials  are  subject  to  market  changes, 
but  are  usually  about  as  follows :  nitrate  of  soda,  30  per 
pound  in  200-pound  bags ;  muriate  of  potash,  30  per  pound 
in  200-pound  bags ;  and  acid  phosphate,  10  per  pound  in 
125-pound  bags. 

62.  A  complete  fertilizer  (one  containing  all  the  ingredi- 
ents) is  quite  often  unnecessary  and  expensive.    A  crop  of 
clover  or  other  legumes  may  supply  the  soil  with  all  the 
nitrogen  needed  for  the  next  crop.    In  this  case  phosphoric 
acid  and  potash  are  the  only  fertilizing  elements  necessary. 

A  farmer  can  make  at  home  100  Ib.  of  2-8-4  fertilizer 

1 

from  nitrate  of  soda  containing  15  %  of  nitrogen,  acid  phos- 
phate containing  16%  of  phosphoric  acid,  and  muriate  of 
potash  containing  50%  of  potash  as  follows  : 

The  mixture  must  contain  2%  nitrogen,  8%  phosphoric  acid,  and 
4%  potash. 

2%  of  100  Ib.  =  2  Ib.,  amount  of  nitrogen  required. 

8%  of  100  Ib.  =  8  Ib.,  the  amount  of  phosphoric  acid  required. 

4%  of  100  Ib.  =  4  Ib.,  the  amount  of  potash  required. 

(1)  Since  only  15%  of  the  nitrate  of  soda  is  nitrogen,  the  2  Ib.  of 
nitrogen  is  15%  of  the  amount  of  nitrate  of  soda  required  for  the  mix- 
ture, or  13  J  Ib.  of  nitrate  of  soda. 

(2)  Since  only  16%  of  the  acid  phosphate  is  phosphoric  acid,  the  8  Ib. 
of  phosphoric  acid  is  16%  of  the  amount  of  acid  phosphate  required 
for  the  mixture,  or  50  Ib.  of  acid  phosphate. 


52  CONSEEVATION  OF  THE  SOIL 

(3)  Since  only  50%  of  the  muriate  of  potash  is  potash,  the  4  Ib.  of 
potash  is  50%  of  the  amount  of  muriate  of  potash  required  for  the 
mixture,  or  8  Ib.  of  muriate  of  potash. 

(4)  To  the  71  ^lb.  of  nitrate  of  soda,  phosphoric  acid,  and  muriate 
of  potash  must  be  added  also  28 §  Ib.  of  sand  or  dry  dirt,  called  filler, 
to  make  the  proper  per  cent. 


EXERCISE 

1.  In  a  125-pound  sack  of  2-10-2  fertilizer  there  are  how 
many  pounds  each  of  nitrogen,  phosphoric  acid,  and  potash  ? 

2.  In  a  ton  of  4-8-4  fertilizer  there  are  how  many  pounds 
each  of  nitrogen,  phosphoric  acid,  and  potash  ? 

3.  Make  1  ton  of  wheat  and  corn  3-10-3  fertilizer  from 
nitrate  of  soda  containing  15%  of  nitrogen,  acid  phosphate 
containing  16%  of  phosphoric  acidj  and  muriate  of  potash 
containing  50%  of  potash.    How  much  filler  must  be  used  ? 

4.  From  data  given  in  paragraph  61,  estimate  the  cost 
of  the  material  for  making  1  ton  of  4~8~4  potato  fertilizer ; 
1  ton  of  2~5~8  tobacco  fertilizer ;  1  ton  of  2~8~7  potato 
fertilizer ;  1  ton  of  2-10-2  grain  fertilizer.  How  much  filler 
is  used  with  each  ton  ? 

5.  Bring  to  school  a  number  of  labels  taken  from  fertil- 
izer sacks   at  home,  and   from   the   data  previously  given 
estimate  the  cost  of  the  material  for  making  1  ton.    Find 
the  local  dealer's  price  on  each  brand,  and  estimate  the 
saving  on  each  ton  by  mixing  it  at  home. 

6.  Cottonseed  meal  that  contains  5j%  of  nitrogen,  2%  of 
phosphoric  acid,  and  1^%  of  potash  is  worth  how  much  per 
ton  if  nitrogen  is  20$  per  pound,  phosphoric  acid  4$  per 
pound,  and  potash  4$  per  pound  ? 

7.  If  a  farmer  puts  400  Ib.  of  fertilizer  valued  at  $24  per 
ton  on  1  A.  of  corn,  how  many  additional  bushels  of  corn 
worth  50$  per  bushel  must  he  raise  to  pay  for  the  fertilizer  ? 


DRAINAGE  53 

8.  If  a  crop  of  potatoes  following  a  clover  crop  requires 
a  special  fertilizer,  0-8-7,  instead  of  a  2—8-7,  using  the  pre- 
ceding data  for  the  cost  of  material,  estimate  the  saving  on 
5  tons  of  special  fertilizer. 

9.  What  is  the  difference  in  the  cost  of  a  4-8-4  and  a 
0-8-4  fertilizer  ? 

DRAINAGE 

63.  Low  and  wet  land  not  suitable  for  farming  can  usu- 
ally be  made  into  rich  and  productive  fields  by  a  proper 
system  of  drainage. 

EXERCISE 

1.  A  fall  of  6  in.  for  each  hundred  feet  is  considered  a  good 
grade  for  farm  drainage.    How  much  fall  is  this  to  the  rod  ? 

2.  A  fall  of  3  in.  for  each  hundred  feet  is  considered  a 
minimum  grade  for  farm  drainage.    How  much  fall  is  this 
to  the  rod  ? 

3.  A  40-acre  field  in  the  form  of  a  square  is  5  ft.  higher  at 
one  end  than  at  the  other.    How  much  fall  is  this  to  the  rod  ? 

4.  If  4-inch  tiling  1  ft.  long  costs  $20  per  1000,  and  the 
cost  to  dig  the  ditch,  lay  the  tile,  and  fill  the  ditch  is  250 
per  rod,  what  will  it  cost  to  tile  a  field  40  rd.  by  80  rd.,  if 
the  tiles  are  run  in  strings  lengthwise  of  the  field  and 
placed  4  rd.  apart,  the  outside  ones  being  2  rd.  from  either 
side  ?   How  much  is  this  per  acre  ? 

5.  With  wheat  at  $1  per  bushel,  what  must  be  the  in- 
crease in  yield  per  acre  to  make  it  possible  to  pay  half  the 
expense  of  tiling  the  land  in  2  years'  time  ? 

6.  With  corn  at  400  per  bushel,  what  must  be  the  increase 
in  yield  per  acre  to  make  it  possible  to  pay  the  remaining 
expense  of  tiling  the  land  in  2  yr.  more  ? 

7.  What  per  cent  did  the  farmer  make  on  the  expense  of 
the  tiling  ? 


HOUSEHOLD  AND  HEALTH  PROBLEMS 
SEWING 

64.  Several  dollars  a  year  can  be  saved  in  providing  for 
a  family  by  knowing  the  quality,  quantity,  and  the  proper 
season  for  buying  food  and  clothing. 

EXERCISE 

1.  If  it  takes  3J  yd.  of  25-cent  material  and  5  cents' 
worth  of  thread  and  buttons  to  make  a  man's  shirt  that 
might  be  bought  ready-made  for  $1.50,  what  is  saved  by 
making  the  shirt  at  home  ? 

2.  How  many  yards  of  27-inch  goods  will  be  required  for 
a  flounce  on  a  skirt  that  measures  2  J  yd.  around  the  bottom, 
if  the  flounce  is  to  be  cut  8  in.  wide  and  one  third  is  allowed 
for  fullness  ? 

3.  How  many  yards  of  soutache  braid  are  required  for 
5  rows  around  a  boy's  sailor  collar,  the  distance  around  the 
collar  being  39  in.  ? 

4.  How  many  yards  of  sheeting  2\  yd.  wide  must  be  bought 
to  make  6  sheets,  if  each  sheet  is  to  measure  2\  yd.  finished, 
with  a  1-inch  hem  at  one  end  and  a  2j-inch  hem  at  the  other, 
and  3  in.  is  allowed  for  shrinkage  ? 

5.  How  long  must  a  skirt  be  cut  to  measure  39  in.  when 
finished,  if  it  has  two  clusters  of  tucks  each  composed  of 
five  ^-inch  tucks,  and  is  lengthened  by  a  6-inch  flounce  ? 
(Allow  J  in.  for  adding  the  flounce.) 

54 


FOOD  55 

6.  If  8  yd.  of  goods  27  in.  wide  will  make  a  dress,  how 
many  yards  of  goods  36  in.  wide  will  it  take  ? 

SUGGESTION.  (1)  When  wider  material  is  to  be  used,  multiply  the 
number  of  yards  required  of  the  narrower  material  by  its  width  in 
inches,  and  divide  the  product  by  the  width  in  inches  of  the  wider 
material. 

(2)  When  narrower  material  is  to  be  used,  multiply  the  number  of 
yards  required  of  the  wider  material  by  its  width  in  inches,  and  divide 
the  product  by  the  width  in  inches  of  the  narrower  material. 

7 .  If  6  yd.  of  material  36  in.  wide  will  make  a  dress,  how 
many  yards  of  material  44  in.  wide  will  it  take  ;  of  material 
54  in.  wide  ? 

8.  Woolen  dress  goods  of  the  same  quality  is  offered 
at  500  per  yard  in  a  36-inch  width,  and  at  750  per  yard 
in  a  54-inch  width.    If  it  takes   6  yd.  of  36-inch  goods, 
what  is  the  cost  of  the  dress  when  made  from  the  54-inch 
goods  ? 

9.  Which  is  the  cheaper  to  buy  for  a  dress,  8  yd.  of  linen 
27  in.  wide  at  150  per  yd.,  or  linen  36  in.  wide  at  250  per 
yard? 

10.  Which  is  the  cheaper  to  buy  for  a  dress,  7  yd.  of 
goods  27  in.  wide  at  350  per  yd.,  or  goods  of  the  same 
quality  54  in.  wide  at  650  per  yard? 

FOOD 

65.  If  the  body  is  to  do  efficient  work,  it  must  be  prop- 
erly fed.    It  is  important,  therefore,  that  the  child  should 
understand  something  of  the  value  of  food,  its  elements,  and 
its  use  in  the  body. 

66.  The  food  substances  are  proteid,  a  muscle  former; 
fat,  a  fuel  to  yield  energy  in  the  form  of  heat  and  muscular 
power ;  carbohydrate,  a  fuel  to  yield  heat  and  energy  or  to 
be  transformed  into  fat ;  and  mineral  matter,  a  bone-tissue 
former. 


56      HOUSEHOLD  AND  HEALTH  PEOBLEMS 


67.  Food    substances    and    their    percentages   found   in 
different  foods  are  about  as  follows : 


Name 

Proteid 

Carbo- 
hydrate 

Fat 

Water 

Mineral 
matter 

Milk  

3.3 

5. 

4. 

87 

7 

Bread  (wheat)   .    .    . 

8.9 

56.7 

4.1 

29.2 

1.1 

Potatoes     ..... 

2.5 

20.9 

.1 

75  5 

1. 

Sweet  potatoes  .    .    . 

1.8 

27.4 

.7 

69. 

1.1 

Butter 

1. 

85 

11 

3 

Esres  . 

13.4 

10.5 

73.7 

1. 

Cheese   

25.9 

2.4 

33.7 

34.2 

3.8 

Chicken     

21.5 

2.5 

74.8 

1.1 

Roast  beef     .... 

22.3 

28.6 

48.2 

1.3 

Smoked  ham     .    .    . 

20.2 

22.2 

Beef,  round  .... 

20.3 

13.6 

65.5 

1.1 

Dried  beans  .... 

22.5 

59.6 

1.8 

12.6 

3.5 

Canned  salmon      .    . 

21.8 

12.1 

63.5 

2.6 

Oatmeal     

16.1 

67.5 

7.2 

7.3 

1.9 

Rice  

8. 

79. 

.3 

12.3 

.4 

Green  corn    .... 

3.1 

19.7 

1.1 

75.4 

.7 

Fresh  cabbage  .    .    . 

1.6 

5.6 

.3 

91.5 

1. 

68.  The  farm  hand  requires  daily  about  4^  oz.  of  proteid, 
4J  oz.  of  fat,  and  16  oz.  of  carbohydrates.  These  food  elements 
are  found  in  widely  different  ratios  in  different  foods.  By  a 
chemical  analysis  of  a  food  it  is  possible  to  find  the  approxi- 
mate quantity  of  that  food  which  must  be  eaten  to  furnish  the 
required  amount  of  proteid,  fat,  or  carbohydrate  for  a  day. 

EXAMPLE.  Wheat  bread  contains  about  8.9%  of  digestible  proteid. 
How  much  bread  will  be  required  to  produce  4 \  oz.  of  proteid  ? 

SOLUTION.   4^  oz.  of  proteid  is  the  amount  required. 
8.9%  of  the  wheat  bread  is  proteid. 
4£  oz.  equals  8.9%  of  the  required  amount  of  bread. 

The  amount  of  proteid  required  divided  by  the  per  cent  of  the 
analysis  expressed  as  a  decimal  gives  the  quantity  of  bread. 
4.5  oz.  -4-  .089  =  47  oz. 


FOOD  57 

EXERCISE 

1.  How  many  pounds  of  wheat  bread  will  it  take  to  pro- 
duce 16  oz.  of  carbohydrate  ? 

2.  How  much  roast  beef  will  it  take  to  produce  4£  oz.  of 
proteid  ? 

3.  How  many  pints  of  milk  will  it  take  to  yield  4£  oz.  of 
fat?  (16oz.  =  lpt.) 

4.  How  much  butter  will  it  take  to  produce  1  oz.  of  fat  ? 

69.  It  is  household  economy  to  be  able  to  work  out  in 
dollars  and  cents  the  comparative  values  of  different  foods. 
This  may  be  done  by  finding  the  cost  of  a  pound  each  of 
proteid,  fat,  and  carbohydrate  in  different  foods. 

EXAMPLE.  If  a  loaf  of  bread  weighing  1  Ib.  sells  for  50,  and  by 
analysis  8.9%  of  it  is  found  to  be  proteid,  what  is  the  cost  of  1  Ib.  of 
proteid  ? 

SOLUTION.   50  =  the  cost  of  8.9%  of  1  Ib. 

The  cost  of  1  Ib.  =  $0.05  -*•  .089  =  $0.56  -. 

EXERCISE 

1.  Find  the  cost  of  1  Ib.  of  proteid  in  milk  which  sells  at 
50  per  quart  and  which  by  analysis  shows  3.4%  proteid. 

2.  Find  the  cost  of  1  Ib.  of  proteid  in  roast  pork  which 
sells  at  12  J0  per  pound  and  which  by  analysis  shows  14% 
proteid. 

3.  Find  the  cost  of  1  Ib.  of  proteid  in  sirloin  steak  which 
sells  at  200  per  pound  and  which  by  analysis  shows  19% 
proteid. 

4.  Which  of  the  above-mentioned  foods  is  the  most  eco- 
nomical muscle-producing  food  ? 

5.  Estimate  which  is  the  cheapest  food  for  producing  fat 
and  heat:  (1)  butter,  which  is  85%  fat,  at  250  per  pound; 


58      HOUSEHOLD  AND  HEALTH  PROBLEMS 

(2)  eggs,  which  are  10%  fat,  at  200  per  dozen  (count  9 
eggs  1  lb.);  (3)  round  steak,  which  is  13%  fat,  at  150  per 
pound ;  (4)  milk,  which  is  5%  fat,  at  50  per  quart  or  2  lb. 

70.  The  cost  of  living  may  be  greatly  increased  by  poor 
preparation  of  food,  unwise  selection  of  foods  for  the  season, 
bad  stoves,  and  waste  of  food. 

EXERCISE 

1.  If  300  is  the  average  daily  cost  per  person  for  raw 
material,  what  is  the  cost  of  the  raw  material  necessary  to 
supply  a  family  of  three  grown  children  and  their  parents 
for  1  yr  ? 

2.  What  would  be  the  increased  cost  of  the  table  supplies 
in  problem  1  if  1\  %  were  added  for  a  bad  oven  and  waste 
of  food  ? 

3.  If  200  is  the  average  daily  cost  per  person  for  raw 
material,  what  will  it  cost  to  supply  the  table  of  a  family 
of  8,  adding  2  %  for  food  wasted  ? 

4.  A  huckster  has  for  sale  a  lot  of  small,  lumpy  potatoes, 
25%  of  which  would  be  lost  in  peeling,  for  450  per  bushel; 
and  a  lot  of  smooth  potatoes,  16 §%  of  which  would  be  lost 
in  peeling,  for  500  per  bushel.    Which  lot  would  prove  the 
better  economy  for  the  buyer  ? 

HEALTH  AND  SANITATION 

71.  Typhoid  fever  is  a  filth  disease.    It  is  impossible  to 
have  it  unless  the  seed,  or  germs,  of  the  disease  are  taken 
into  the  body.    This  happens  only  when  the  water  that 
we  drink  or  the  food  that  we  eat  has  come  in  contact  with 
part  of  the  discharges  of  a  person  who  has  had  the  disease. 
This  is  brought  about  through  the  agency  of  flies,  through 


HEALTH  AND  SANITATION  59 

contaminated  water  —  especially  springs  and  wells  —  and 
through  carelessness  in  handling  food  supplies  —  especially 
milk.  If  the  discharges  from  every  typhoid-fever  patient 
were  thoroughly  disinfected,  every  community  would  be 
free  from  the  disease,  except  when  it  was  brought  from 
outside  its  borders. 

EXERCISE 

1.  The  death  rate  from  typhoid  fever  in  the  United  States 
during  the  year  1910  was  23  out  of  each  100,000  persons. 
What  per  cent  of  the  population  died  from  typhoid  fever  ? 

2.  In  a  certain  state  the  death  rate  from  typhoid  fever 
was  45  out  of  each  100,000  persons.    In  the  year  1911  this 
state  reported  1035  deaths  from  typhoid  fever.    What  was 
the  population  of  the  state  ? 

3.  In  the  state  mentioned  in  problem  2,  the  State  Board 
of  Health  estimated  a  loss  of  $28,450,950  to  the  state  in 
deaths,  doctors7  bills,  and  loss  of  time  of  those  ill  from  pre- 
ventable diseases.  What  was  the  cost  of  this  carelessness  per 
capita,  if  equally  distributed  among  the  entire  population  ? 

4.  In  a  village  of  400  inhabitants  who  were  indifferent 
to  the  laws  of  sanitation,  surface  water  was  allowed  to  seep 
into  the  wells,  surface  closets  were  used,  the  majority  of  the 
kitchens  were  unscreened,  and  flies  in  abundance  visited 
closets  and  kitchens  alike.    During  one  summer  there  were 
5  severe  cases  of  typhoid  fever.    Estimate  what  the  unsani- 
tary conditions  of  the  village  cost  5  citizens,  if  the  expense 
items  were  as  follows  for  each  fever  patient :  84  da.  of  lost 
time  at  $1.50  per  day ;  $30  in  doctors'  bills  ;  3  wk.  of  special 
nursing  at  $20  per  week ;  and  $15  for  other  charges. 

5.  A  prominent  physician  has  estimated  that  the  average 
well  man  loses  5  da.  each  year  from  work  on  account  of  head- 
aches, toothaches,  colds,  and  other  similar  minor  ailments. 


60      HOUSEHOLD  AND  HEALTH  PROBLEMS 

Dr.  L.  H.  Gulick,  an  eminent  authority,  says  that  90%  of 
these  minor  ailments  could  be  prevented  by  careful  atten- 
tion. According  to  the  census  of  1910  there  were  29,000,000 
workers  in  the  United  States.  Estimate  the  loss  of  the  nation 
due  to  carelessness,  if  each  man  could  earn  an  average  of 
$1.25  per  day. 

6.  A  large  optical-goods  factory  in  Germany  reduced  the 
hours  of  its  working  day  from  9^  hr.  to  8  hr.    The  firm 


SANITARY  WELL 

reported,  after  a  careful  record  had  been  kept,  that  the  out- 
put of  the  factory  per  hour  had  been  increased  16.2%.  If 
the  daily  output  of  each  man  working  9^  hr.  per  day  was 
$4.75  worth  of  goods  for  the  market,  what  was  the  value  of 
the  goods  produced  by  the  man  working  8  hr.  per  day?  By 
the  conservation  of  the  employee's  vitality  and  efficiency, 
how  much  productive  wealth  was  added  to  the  output  of 
each  man  per  day. 


HEALTH  AND  SANITATION  61 

7.  It  has  been  authoritatively  estimated  that  a  farm  hand 
infected  with  the  hookworm  disease  is  on  an  average  50% 
less  efficient  in  his  work  than  the  well  man.    Estimate  the 
loss  to  a  county  having  28,500  farmers  and  hired  hands, 
each  man  working  an  average  of  290  da.   a   year  at  $1 
per  day,  if  11%  of  the  men  are  infected  with  the  disease. 
To  cure  each  man  will  not  cost  on  an  average  over  70$. 
Estimate  the  saving  in  1  yr.  from  the  labor  of  these  men 
by  curing  them. 

8.  It  has  been  conservatively  estimated  that,  on  an  aver- 
age, it  takes  the  child  who  attends  school  in  a  house  improp- 
erly heated,  lighted,  and  ventilated  20%  longer  to  complete 
the  common-school  course  of  8  grades  of  8  mo.  each  than 
when  attending  school  in  a  house  that  is  sanitary  and  com- 
fortable in  all  its  appointments.    How  much  time  does  each 
child  lose  in  completing  a  common-school  education  when 
compelled  to  attend  school  in  an  unsanitary  and  uncomfort- 
able house  ? 

9.  In  rural  communities  400,000  persons  die  annually, 
and  about  2,000,000  others  are  seriously  ill  from  infectious 
diseases.    If  only  50%  of  these  deaths  and  cases  of  sickness 
can  be  eliminated  by  normal  schools  and  teachers7  colleges 
in  giving  rural  teachers  special  courses  in  the  first  princi- 
ples of  sanitary  science  and  public  health,  what  would  be 
the  annual  value  of  such  training  to  the  rural  communities 
of  the  United  States,  if  a  human  life  is  rated  at  f  1000  (the 
price  of  a  slave)  and  each  case  of  prevented  sickness  at  $75  ? 


GROWING  CROPS 


IMPORTANT  THINGS    THAT   SHOULD  BE  KNOWN 
ABOUT  SELECTING  SEED  CORN 

72.  The  quality  and  quantity  of  corn  that  is  harvested 
depends  in  a  large  measure  upon  the  care  used  in  selecting 
the  seed.  The  points  to  be  observed  are  as  follows :  (1)  the 


SEED  CORN 

>ar  should  be  selected  from  the  stalk  in  the  fall ;  (2)  the  ear 
should  be  firm ;  (3)  the  ear  should  be  cylindrical  in  shape ; 
(4)  the  ratio  of  the  circumference  of  the  ear  to  its  length 
should  be  about  3  to  4;  (5)  the  butt  should  be  rounded 

62 


SELECTING  SEED  CORN  63 

out  around  a  cup-shaped  cavity ;  (6)  the  shank  should  be 
of  medium  size ;  (7)  the  tip  should  be  filled  out  with  deep 
kernels  in  as  regular  rows  as  possible  ;  (8)  the  kernel  should 
be  uniform  in  size  and  shape,  but  not  pointed ;  (9)  the 
furrows  between  the  rows  should  be  narrow,  with  kernels 
fitting  closely  together  at  the  top ;  (10)  at  least  ±  of  the 
weight  should  be  corn.  From  80  to  100  average  ears  should 
weigh  70  Ib. 

EXERCISE 

1.  In  Holmes  county,  Mississippi,  one  season,  the  mem- 
bers of  the  boys'  corn  club  grew  corn  averaging  76  bu.  per 
acre.    The  corn  grown  by  their  fathers  and  neighbors  aver- 
aged 16  bu.  per  acre.    When  corn  was  selling  at  50$  per 
bushel,  how  much  smarter,  to  the  acre,  were  the  boys  than 
their  neighbors  ? 

2.  How  many  hills  of  corn  are  planted  to  the  acre  when 
the  rows  are  3  ft.  8  in.  apart,  the  hills  in  the  row  being  the 
same  distance  apart  ? 

3.  How  many  stalks  to  the  acre  are  there  when  the  average 
is  2  to  the  hill  ?  when  the  average  is  3  to  the  hill  ? 

4.  Seed  corn  will  average  800  grains  to  the  ear.    How 
many  ears  will  it  take  to  plant  an  acre,  2  grains  to  the  hill, 
when  the  rows  are  3  ft.  8  in.  apart,  the  hills  in  the  row  being 
the  same  distance  apart  ? 

5.  Which  will  produce  the  greater  yield  per  acre :  2  ears 
to  the  hill,  100  ears  making  a  bushel,  or  3  ears  to  the  hill, 
190  ears  making  a  bushel  ? 

6.  If  the  farmer  can  increase  the  weight  of  each  ear  of 
corn  2  oz.  by  proper  selection  of  seed  in  the  fall,  what  will 
the  increase  amount  to  on  a  30-acre  field  averaging  6480 
stalks  per  acre,  with  1  ear  for  each  stalk,  when  corn  is  sell- 
ing at  50$  a  bushel  ? 


64  GKOWING  CEOPS 

7.  When  corn  sells  at  50$  a  bushel,  what  is  the  loss  to 
a  farmer  on  each  bad  ear  of  seed  planted,  if  there  are  800 
grains  of  corn  to  the  ear  and  each  grain  planted  averages 
1  good  ear  such  that  100  make  a  bushel  ? 

8.  If  12  ears  of  properly  selected  seed  corn  will  plant  an 
acre,  how  many  ears  will  it  take  to  plant  a  rectangular  field 
64  rd.  by  30  rd.  ? 

9.  A  farmer  spends  a  half  day  in  selecting  seed  corn  for 
a  5-acre  field.    If  the  increase  in  yield  is  5  bu.  per  acre,  how 
much  does  he  make  at  the  present  price  of  corn  ? 

10.  At  gathering  time  1200  bu.  of  corn  should  weigh 
approximately  how  many  bushels  the  first  of  the  follow- 
ing May  ? 

NOTE.  Corn  shrinks  about  J  of  its  entire  weight  during  the  first 
6  mo.  following  gathering  time. 

11.  A  man  is  offered  500  a  bushel  for  corn  at  gather- 
ing time.    He  holds  the  crop  6  mo.  and  sells  it  at  600  a 
bushel.    How  much  does  he  gain  or  lose  by  holding  a  crop 
of  600  bu.  ? 

12.  A  man  is  offered  at  gathering  time  600  per  bushel 
for  his  corn  crop.    How  much  must  he  receive  per  bushel  so 
that  he  will  neither  lose  nor  gain  by  selling  in  the  spring  ? 

TESTING  SEED  CORN 

73.  Corn  selected  for  seed  should  be  tested  before  plant- 
ing. This  can  be  done  easily.  Make  a  box  36  in.  by  40  in. 
and  2  in.  or  3  in.  deep.  Pill  the  box  about  half  full  of  moist 
dirt,  sand,  or  sawdust.  Press  it  down  so  that  it  will  have 
a  smooth,  even  surface. 

Take  a  white  cloth  about  the  size  of  the  box,  rule  it  off 
into  squares  2  in.  or  3  in.  each  way,  numbering  them  1,  2,  3, 
4,  etc.,  and  place  it  in  the  box  upon  the  sand. 


TESTING  SEED  CORN  65 

Carefully  remove  5  or  6  grains  from  each  ear  of  corn, 
place  them  in  the  numbered  squares  corresponding  to  the 
numbers  on  the  ears,  and  cover  with  a  flour  sack  padded 
with  about  2  in.  of  moist  sand  or  sawdust.  Place  the  box  in 


TESTING  SEED  CORN  FOR  TEN  ACRES 

a  warm  place  where  it  will  not  get  chilled.  Keep  the  pad 
well  dampened  and  warm,  and  in  five  or  six  days  remove 
the  pads  carefully.  Select  for  seed  those  ears  whose  grains 
have  both  sprouts  and  rootlets. 

EXERCISE 

1.  When  corn  is  selling  at  750  a  bushel,  what  is  a  farmer's 
loss  by  planting  one  bad  ear  of  seed  corn  ? 

2.  When   corn  is  selling  at  600  a  bushel,  what  is   the 
loss  to  a  neighborhood  by  planting  50  bad  ears  of  seed 
corn  ? 

3.  A  farmer,  by  planting  only  tested  corn,  may  depend 
upon  an  increase  of  5  bu.  per  acre.    If  your  father  did  not 
test  his  seed  last  spring,  estimate  his  loss  at  the  present 
price  of  corn. 


66  GROWING  CEOPS 

4.  The  children  of   the  public   schools  can  do  all  the 
testing  for  their  own  district.    Find  out  how  many  acres 
of  corn  were  planted  in  your  district  last  year  and  esti- 
mate, at  the  present  price  of  corn,  how  much  the  school 
could  have  earned  for  your  neighborhood  by  testing  its 
seed  corn. 

5.  If  a  clean  field  produces  60  bu.  of  corn  per  acre  and 
a  weedy  one  only  40  bu.,  what  is  the  loss  per  acre  caused  by 
weeds,  with  corn  at  35$  a  bushel  ?    Suppose  4  days'  work 
would  keep  an  acre  clean,  how  much  would  1  day's  work 
profit  the  farmer  ? 

6.  A  field  of  oats  clear  of  weeds   produces   50  bu.  per 
acre.    If  a  weedy  field  produces  only  37  bu.,  what  is  the 
loss  on  1  A.  of  weedy  oats  when  oats  sell  at  25$  a  bushel  ? 

7 .  In  a  demonstration  a  field  plowed  4  in.  deep  produced 
30  bu.  of  corn  per  acre,  and  a  field  plowed  6  in.  deep  pro- 
duced 42  bu.  of  corn  per  acre.    At  the  present  price  of  corn, 
determine  the  value  of  the  deep  plowing  on  one  acre ;  on  a 
40-acre  field  of  corn. 

8.  If  a  man  charges  $2.50  a  day  for  plowing,  what  is  the 
difference  in  the  cost  of  plowing  the  field  in  the  above  prob- 
lem if  in  one  day  the  man  can  plow  2^  A.,  4  in.  deep,  or 
11  A.,  6  in.  deep.    At  the  present  price  of  corn,  does  deep 
plowing  pay  ? 

9.  Seventy-five  bushels  of  corn  per  acre  would  be  a  good 
yield  when  the  land  is  plowed  deep  and  carefully  culti- 
vated ;   and  30  bu.  a  fair  yield  when  the  land  is  plowed 
shallow  and  only  reasonably  well  cultivated.    If  a  man  is 
able  to  cultivate  20  A.  thoroughly  or  35  A.  carelessly,  by 
which  method  of  cultivation  would  he  realize  more  when 
corn  is  worth  40$  a  bushel  ?    What  important  consideration 
has  been  left  out  of  this  problem  ? 


COST  OF  GKOWING  COEK  67 

10.  How  many  cubic  feet  of  cultivated  soil  are  there 
in  1  A.  if  soil  is  cultivated  4  in.  deep  ?  if  soil  is  cultivated 
6  in.  deep  ? 

11.  If  a  cubic  foot  of  soil  weighs  75  Ib.  and  contains 
3^  oz.  of  nitrogen,  1 J  oz.  of  phosphoric  acid,  and  4  oz.  of 
potash,  find  the  number  of  pounds  of  each  of  these  ferti- 
lizing substances  in  1  A.  of  cultivated  soil  4  in.  deep ;  6  in. 
deep ;  8  in.  deep.    Why  plow  deep  ? 

12.  How  much  more  plant  food  is  made  available  by  culti- 
vating the  soil  6  in.  deep  than  by  cultivating  it  4  in.  deep  ? 

COST  OF  GROWING  CORN  ON  ROUGH  LAND 

74.  The  farmer  should  know  the  cost  of  growing  a  bushel 
of  corn  on  his  farm.  This  will  enable  him  to  determine  to 
what  extent  he  should  grow  corn. 

EXERCISE 

1.  Estimate  the  cost  of  growing  a  15-acre  field  of  corn 
when  (1)  a  man  with  a  two-horse  plow  can  break  1£  A. 
per  day ;  (2)  a  man  with  a  one-horse  plow  can  lay  off  8  A. 
per  day  ;  (3)  a  man  can  plant  5  A.  per  day ;  (4)  a  man  with 
double  shovel  can  cultivate  3  A.  per  day ;  (5)  a  man  can 
hoe  1  A.  per  day ;  (6)  the  corn  is  to  be  cultivated  3  times ; 
(7)  the  corn  is  to  be  hoed  twice;   (8)  a  man  with  team 
and  wagon  and  2  helpers  can  gather  3  A.  per  day ;  (9)  a 
man  with  a  team  is  paid  $3  per  day  and  given  2  meals ; 
(10)  a  man  with  a  horse  is  paid  $1.50  per  day  and  given 
2  meals  ;  (11)  a  man  working  alone  is  paid  750  per  day  and 
given  2  meals ;  (12)  meals  for  men  are  reckoned  at  150,  for 
horses  at  150 ;  (13)  seed  corn  costs  300  per  acre. 

2.  The  yield  being  25  bu.  per  acre,  what  was  the  cost  per 
bushel  to  grow  corn  in  problem  1  ? 


68  GROWING  CROPS 

3.  At  the  present  price  of  corn,  is  it  better  for  the  renter 
to  give  a  third  of  the  crop  as  rent/ or  to  pay  $2  cash  per 
acre  and  take  all  the  corn  ? 

4.  The  conditions  stated  above  hold  for  a  county  whose 
corn  crop  averaged  17^  bu.  per  acre  for  the  year  1911.  What 
was  the  average  cost  of  growing  each  bushel  of  corn  ? 

COST  OF  GROWING  CORN  ON  SMOOTH  LAND 

75.  The  merchant  who  does  not  know  the  cost  of  his 
goods  cannot  reasonably  hope  to  be  successful.  The  farmer 
should  be  as  familiar  with  the  cost  of  producing  his  farm 
products  as  he  is  with  their  market  prices. 

EXERCISE 

1.  Estimate  the  cost  of  growing  a  30-acre  field  of  corn 
in  the  corn  belt  when  (1)  a  man  with  a  two-horse  plow 
can  break  2  A.  per  day ;  (2)  a  man  with  a  three-horse  disk 
harrow  can  disk  7-^  A.  per  day ;  (3)  a  man  with  a  three- 
horse  harrow  can  harrow  15  A.  per  day ;  (4)  a  man  with 
planter  can  plant  12  A.  per  day ;  (5)  a  man  with  cultivator 
can  cultivate  5  A.  per  day ;  (6)  two  men  with  a  wagon  and 
team  can  gather  3  A.  per  day ;  (7)  the  com  is  to  be  culti- 
vated 5  times ;  (8)  a  man  with  a  team  is  paid  $3  per  day ; 
(9)  a  man  working  alone  is  paid  $1  per  day ;  (10)  thirty 
cents'  worth  of  seed  corn  per  acre  is  used. 

2.  The  yield  being  60  bu.  per  acre,  what  was  the  cost  per 
bushel  to  grow  the  corn  in  the  above  problem  ? 

3.  At  the  present  price  of  corn,  is  it  better  for  the  renter 
to  give  f  of  the  crop  as  rent,  or  to  pay  $3  per  acre  for 
the  use  of  the  land  ?  How  much  per  acre  does  the  owner 
of  the  land  realize  if  he  receives  f  of  the  crop  as  rent? 
J  of  the  crop  as  rent  ? 


COST  OF  GROWING  COTTON  69 

COST  OF  GROWING  WHEAT 

76.  The  improved  machinery  now  used  for  planting  and 
harvesting  wheat  has  greatly  reduced  the  expense  of  grow- 
ing wheat. 

EXERCISE 

1.  Estimate  the  cost  of  growing  a  20-acre  field  of  wheat 
when  (1)  a  man  with  a  two-horse  plow  can  break  2  A.  per 
day ;  (2)  a  man  with  a  three-horse  harrow  can  harrow  15  A. 
per  day ;  (3)  a  man  with  a  three-horse  roller  can  roll  12  A. 
per  day  ;  (4)  a  man  with  a  two-horse  drill  can  drill  10  A.  per 
day ;  (5)  the  seed  per  acre  is  worth  $1.50 ;   (6)  the  land  is 
harrowed  twice  and  rolled  once ;  (7)  a  man  with  a  team  is 
paid  $3  per  day  ;  (8)  the  cost  of  fertilizing  each  acre  is  $1.50 ; 

(9)  the  cost  of  putting  the  wheat  in  the  shock  is  $1  per  acre ; 

(10)  the  cost  of  threshing  the  wheat  is  60  per  bushel. 

2.  The  yield  being  20  bu.  per  acre,  what  was  the  cost  per 
bushel  to  grow  the  wheat  in  the  above  problem  ? 

3.  Using  10  men  3  da.  at  $1.50  per  day  and  45  bu.  coal 
at  150  per  bushel,  estimate  the  cost  of  threshing  800  bu. 
wheat  @  40  per  bushel,  1000  bu.  oats  @  20  per  bushel,  200  bu. 
flax  @  80  per  bushel,  100  bu.  timothy  @  200  per  bushel. 

COST  OF  GROWING  COTTON 

77.  Cotton  is  a  staple  crop  of  the  South.    It  is  valuable 
both  for  the  lint  and  the  seed  it  yields. 

EXERCISE 

1.  If  a  20-acre  field  yields  840  Ib.  of  seed  cotton  per 
acre  and  this  cotton  when  ginned  yields  40%  lint,  what  is 
the  seed  worth  at  900  per  hundred  and  the  cotton  at  $54  per 
bale  of  500  Ib.  each,  the  weight  of  the  bale  including  20  Ib 
for  bagging  and  ties  ? 


70  GEOWING  CEOPS 

2.  If,  in  the  preceding  problem,  the  cost  of  preparing  the 
land  and  cultivating  the  cotton  was  $15  per  acre,  fertilizer 
$6.50  per  acre,  picking  50$  -per  hundred,  and  ginning,  bag- 
ging, and  ties  $1.60  per  bale,  what  was  the  net  cost  per 
100  Ib.  of  raising  the  cotton  ? 

3.  If  seed  cotton   yields  40%    lint  when   ginned,  how 
many  pounds  of  cotton  in  the  seed  will  it  take  to  make  a 
520-pound  bale,  including  20  Ib.  for  bagging  and  ties  ? 

4.  A  30-acre  field  of  cotton  produced  1155  Ib.  of  seed 
cotton  per  acre.    If  the  ginned  cotton  yielded  33 J%  lint, 
how  much  was  the  cotton  worth  at  12|$  per  pound? 

5.  At  an  experiment  station  land  that  was  plowed  8  in. 
deep  yielded  1160  Ib.  of  seed  cotton  per  acre,  and  land  plowed 
4  in.  deep  yielded  950  Ib.    If  the  ginned  cotton  yielded  35% 
lint,  and  was  worth  12$  per  pound,  and  the  seed  was  worth 
90$  per  hundred,  what  was  the  value  of  the  deep  plowing 
per  acre  ? 


ESTIMATION  OF  CROPS  IN  THE  BULK 
CORN 

78.  Approximately  3^  cu.  ft.  of  corn   in  the  husk  and 
2jcu.  ft.  on  the  cob  make  a  bushel. 

There  are  2150.4  cu.  in.  of  shelled  corn  in  a  bushel. 

79.  The  capacity  of  a  crib  in  bushels  equals  the  product 
of  the  length,  width,  and  depth  in  feet  divided  by  3|  for 
corn  in  the  husk,  and  by  2j  for  corn  on  the  cob. 

80.  Rule.    To  find  the  number  of  bushels  of  corn  in  the  husk 
in  a  round  pile,  square  ±  the  distance  across  the  pile  in  feet 
and  multiply  by  3±;  then  multiply  by  j  the  height  of  the  p He 
in  feet  and  divide  by  3^. 

EXERCISE 

1.  How  many  bushels  of  corn  in  the  husk  are  there  in  a 
crib  12  ft.  long,  8  ft.  wide,  and  7  ft.  high  ? 

2.  How  many  bushels  in  the  husk  will  a  rail  pen  7£  ft. 
long,  7^  ft.  wide,  and  9  ft.  high  hold  ? 

3.  Measure  the  crib  at  home  and  estimate  how  many 
bushels  it  will  hold.    How  many  bushels  are  in  it  now  ? 

4.  Measure  the  wagon  box  at  home  and  estimate  the 
number  of  bushels  it  will  hold. 

5.  How  high  must  a  crib  10ft.  long  and  8ft.  wide  be 
built  to  hold  150  bu.  ? 

6.  How  many  bushels  of  corn  in  the  husk  are  there  in  a 
round  pile  12  ft.  across,  tapering  to  a  point  6  ft.  high  in  the 
middle  ? 

71 


72      ESTIMATION  OF  CROPS  IN  THE  BULK 

7.  How  many  bushels  of  ear  corn  will  a  wagon  bed  that 
is  10  ft.  long,  3  ft.  wide,  and  26  in.  deep  hold  ? 

8.  How  many  bushels  of  corn  in  the  husk  will  the  crib 
at  home  hold?    How  many  bushels  of  corn  on  the  cob  will 

it  hold? 

HAY 

81 .  A  ton  of  packed  timothy  hay  contains  about  450  cu.  ft. ; 
a  ton  of  clover,  alfalfa,  or  cowpea  hay,  about  550  cu.  ft. 

82.  The  capacity  of  a  hayloft  in  tons  equals  the  product 
of  the  length,  width,  and  height  in  feet,  divided  by  450  for 
timothy  hay,  and  by  550  for  clover  hay. 

83.  Rule.    To  find  the  approximate  number  of  tons  in  a 
stack,  square  j  of  the  distance  around  the  stack,  measured  at 
a  point  halfway  from  the  ground  to  the  top  ;  multiply  this  by 
the  height  of  the  stack  in  feet,  and  divide  by  450  if  timothy 
hay ;  by  550  if  clover,  alfalfa,  or  cowpea  hay.  For  ricks :  Meas- 
ure over  the  rick,  from  the  ground  on  one  side  to  the  ground  on 
opposite  side  ;  also  the  ividth  of  stack  near  the  ground.  Add 
the  over  measure  and  the  width  together ;  divide  by  4;  square 
the  result  and  'multiply  by  the  length  of  rick  ;  then  divide  by 
450  if  timothy  ;  by  550  if  clover,  alfalfa,  or  cowpea  hay. 

EXERCISE 

1.  How  many  tons  of  timothy  hay  are  there  in  a  loft 
30  ft.  long,  24  ft.  wide,  with  an  average  depth  of  7  ft.  ? 

2.  Measure  and  estimate  the  number  of  tons  of  timothy 
hay  that  your  barn  will  hold. 

3.  How  many  tons  of  clover  hay  can  be  stored  in  a  place 
15  ft.  long,  12  ft.  wide,  and  6  ft.  deep? 

4.  Measure  a  number  of  haystacks  in  your  neighborhood 
and  estimate  the  approximate  number  of  tons  in  each  stack. 

5.  Measure  one  of  your  father's  or  neighbor's  haystacks 
and  estimate  its  worth  at  the  local  price  of  hay. 


APPLES  AND  POTATOES  73 

APPLES  AND  POTATOES 

84.  Apples,  potatoes,  turnips,  etc.  are  measured  by  the 
heaped  bushel  (2747.7  cu.  in.),  but  for  practical  purposes 
it  is  sufficiently  accurate  to  take  If  cu.  ft.  as  a  bushel. 


STRICKEN  MEASURE  HEAPED  MEASURE 

85.  Rule.  To  find  the  number  of  bushels  in  a  round  pile 
of  apples,  potatoes,  etc.,  square  j  the  distance  across  the  pile 
in  feet,  multiply  by  3^,  then  by  j  the  height  of  the  pile  in 
feet,  and  take  j  of  the  product. 

EXERCISE 

1.  How  many  bushels  of  potatoes  can  be  put  in  a  wagon 
bed  10  ft.  long,  3  ft.  wide,  and  16  in.  deep  ? 

2.  How  many  bushels  of  apples  can  be  put  in  a  box  4  ft. 
long,  3  ft.  wide,  and  2  ft.  deep  ? 

3.  When  potatoes  are  selling  at  50$  per  bushel,  what  is  the 
value  of  a  round  pile  which  is  10  ft.  across  at  the  bottom, 
and  tapers  to  a  point  6  ft.  high  in  the  middle  ? 

4.  How  many  bushels  of  apples  are  there  in  a  round 
pile  12  ft.  across,  which  tapers  to  a  point  5  ft.  high  in  the 
middle  ? 

5.  Measure  and  estimate  the  bushels  of  apples,  potatoes, 
turnips,  etc.  holed  up  at  home. 


74      ESTIMATION  OF  CKOPS  IN  THE  BULK 

6.  How  many  bushels  will  a  wagon  bed  10  ft.  long,  3  ft. 
wide,  and  2  ft.  deep  hold  ? 

7.  A  huckster  in  selling  apples  gives  stricken  measure 
(2150.4  cu.  in.)  instead  of  heaped  measure.   In  selling  23  bu. 
of  apples  at  $1  per  bushel,  he  cheats  his  customers  out  of 
how  much  money  ? 

8.  A  grocer  pays  $1.20  per  bushel  for  apples  which  he 
retails  at  3  for  5$.    The  apples  average  96  to  the  bushel. 
What  per  cent  does  he  make  on  the  sale  of  each  bushel  if 
10%  of  the  selling  price  is  the  expense  of  handling? 

9.  A  grocer  uses  a  half-peck  measure  6  in.  in  diameter. 
What  is  the  height  of  the  measure  ? 

10.  A  grocer  uses  a  peck  measure  7  in.  in  diameter.  What 
is  the  height  of  the  measure  ? 

11.  A  farmer  sold  .2  ton  of  hay  for  $2.50.    What  was 
the  value  of  the  hay  per  ton  ? 

12.  A  farmer  sold  his  hay  at  the  barn.    The    average 
weight  of  each  bale  was  determined  by  weighing  15  repre- 
sentative bales.    Their  combined  weight  was  1320  Ib.    How 
many  bales  would  a  purchaser  of  2|  tons  receive  ? 


STOCK  AND   FEED   PROBLEMS 


KINDS  AND  QUANTITIES  OF  FEED 

86.  The  value  of  any  feed  lies  in  the  food  elements  which  it 
contains.  These  elements  are  protein,  fats,  and  carbohydrates. 

The  work  horse  and  the  cow  of  average  size  require  daily 
about  2  Ib.  of  protein  and  12  Ib.  of  carbohydrates.  The 
amount  of  any  feed  to  be  given  depends  largely  upon  the 
quantity  of  the  elements  that  it  contains.  From  the  table 
below  it  will  be  seen  that  cottonseed  meal,  for  instance,  is 
much  richer  in  protein  and  carbohydrates  than  is  wheat 
bran ;  so  a  smaller  quantity  of  it  should  be  fed  to  obtain 
the  same  amount  of  food. 

87.  This  table  gives  the  percentage  of  digestible  protein 
and  carbohydrates  contained  in  certain  feeds : 


Name  of  feed 

Protein 

Carbo- 
hydrates 

Corn  fodder    

2  5 

35  5 

Timothy  hay  

2.75 

46 

Hedtop  liny 

4  75 

49 

Clover  hay       .    .                              ... 

8  5 

46 

Cowpea  hay    

10  5 

40 

Oat  straw    

1.2 

46 

Wheat  straw 

5 

36 

Wheat  bran 

12 

45 

Cottonseed  meal              .            ... 

40 

40 

Corn    

7  8 

78  2 

Oats     . 

9  2 

57  8 

Corn  ensilage 

9 

13 

NOTE.   One  Ib.  of  fat  is  equivalent  to  about  2J  Ib.  of  carbohydrates. 

75 


76  STOCK  AND  FEED  PEOBLEMS 

EXAMPLE.  How  much  cottonseed  meal  must  be  fed  a  cow  that 
she  may  get  2  Ib.  of  protein  ? 

SOLUTION.   2  Ib.  of  protein  is  the  amount  required. 
40%  of  the  cottonseed  meal  is  protein. 
2  Ib.  equals  40%  of  the  required  amount  of  cottonseed 

meal. 
2  Ib.  -=-  .40  =  5  Ib.,  the  required  amount. 

88.  Rule.  To  determine  how  much  feed  is  required  to  obtain 
a  given  amount  of  a  food  element -,  divide  the  required  amount 
of  the  food  element  by  its  per  cent  in  the  analysis  expressed 
as  a  decimal. 

EXERCISE 

Study  the  above  table  and  answer  the  following  questions  : 

1.  If  timothy  and  redtop  hay  are  selling  for  the  same 
price  per  100  Ib.,  which  is  the  cheaper  feed  for  a  horse  ? 

2.  When  timothy,  redtop,  and  clover  hay  are  selling  at 
the  same  price  per  ton,  which  is  the  cheapest  cow  feed  ? 

3.  How  much  wheat  bran  must  a  cow  be  fed  that  she 
may  get  2  Ib.  of  protein  ? 

4.  If  a  cow  is  fed  daily  10  Ib.  of  bran,  how  much  clover 
hay  must  be  fed  that  the  cow  may  have  at  least  2  Ib.  of 
protein  ? 

5.  How  many  pounds  of  oats  must  be  fed  a  horse  that  he 
may  have  2  Ib.  of  protein  ? 

6.  How  many  ears  of  corn  (100  ears,  or  56  Ib.,  to  the  bushel) 
must  be  fed  a  horse  that  he  may  have  2  Ib.  of  protein  ? 

7.  Which  is  the  cheaper  feed  for  a  work  horse  during 
summer,   oats  (32  Ib.  per  bu.)  at  250  per  bu.  or  corn  at 
400  per  bu.,  disregarding  the  carbohydrates  ?    (Use  data  in 
problems  5  and  6.) 

8.  What  is  the  cost  per  pound  of  protein  in  cowpea  hay 
at  $10  per  ton  ?  in  clover  hay  at  $10  per  ton  ? 


KINDS  AND  QUANTITIES  OF  FEED          77 

89.  The  nutritive  ratio  of  any  feed  is  the  ratio  of  its 
protein  to  its  carbohydrates. 

90.  Rule.    To  find  the  nutritive  ratio  of  two  or  more  differ- 
ent feeds  when  fed  in  combination,  take  the  sum  of  the  pro- 
tein in  the  combined  feeds  as  the  antecedent  of  a  ratio  in 
which  the  sum  of  the  carbohydrates  is  the  consequent,  and 
reduce  the  ratio  to  its  lowest  terms. 

EXAMPLE.  What  is  the  nutritive  ratio  of  a  ration  consisting  of 
10  Ib.  of  corn,  31b.  of  cottonseed  meal,  and  15  Ib.  of  timothy  hay  ? 

SOLUTION.  From  the  table  it  is  seen  that  7.8  Ib.  of  every  100  Ib. 
of  corn  is  protein  and  78.2  Ib.  carbohydrates.  Then  10  Ib.  would  con- 
tain .1  of  the  protein  and  carbohydrates  in  100  Ib. 


.1  of  7.81b.=  .781b.  protein. 
.1  of  78.2  Ib.  =  7.82  Ib.  carbohydrates. 


From  the  table  it  is  seen  that  40  Ib.  of  every  100  Ib.  of  cottonseed 
meal  is  protein  and  40  Ib.  carbohydrates.  Then  3  Ib.  would  contain 
.03  of  the  protein  and  carbohydrates  in  100  Ib. 

.03  of  40  Ib.  =  1.2  Ib.  protein. 

.03  of  40  Ib.  =  1.2  Ib.  carbohydrates. 

From  the  table  it  is  seen  that  2.75  Ib.  of  every  100  Ib.  of  timothy 
hay  is  protein  and  46  Ib.  carbohydrates.  Then  15  Ib.  would  contain 
.15  of  the  protein  and  carbohydrates  in  100  Ib. 

.15  of  2.751b.  =  .4125  Ib.  protein. 

.15  of  46  Ib.  =  6.9  Ib.  carbohydrates. 

.78  Ib.  +  1.2  Ib.  +  .4125  Ib.  =  2.3925  Ib.  protein. 

7.82  Ib.  +  1.2  Ib.  +  6.9  Ib.  =  15.92  Ib.  carbohydrates. 

Making  the  protein  the  antecedent  and  the  carbohydrates  the 
consequent  of  a  ratio,  we  have  2.3925  : 15.92  =  6.  The  nutritive  ratio 
is  1 :  6. 

NOTE.  A  ratio  may  be  reduced  to  its  lowest  terms  by  dividing  each 
term  by  the  antecedent. 


78  STOCK  AND  FEED  PROBLEMS 

EXERCISE 

1.  What  is  the  nutritive  ratio  of  a  ration  consisting  of 
1  bu.  of  oats  mixed  with  1  bu.  of  corn  ? 

2.  What  is  the  nutritive  ratio  of  a  ration  consisting  of 
5  Ib.  of  corn,  1  Ib.  of  cottonseed  meal,  8  Ib.  of  cowpea  hay, 
and  30  Ib.  of  corn  ensilage  ? 

3.  What  is  the  nutritive  ratio  of  100  Ib.  of  wheat  bran 
and  1  bu.  of  corn  ?    Is  this  a  suitable  cow  feed  if  a  nutritive 
ratio  of  about  1 : 6  is  a  balanced  ration  for  a  dairy  cow  ? 

4.  What  is  the  cost  of  feeding  a  work  team  56  ears  of 
corn  per  day  during  January,  at  50$  per  bushel  (100  ears  to 
the  bushel),  and  32  Ib.  of  timothy  hay  daily  at  $12  per  ton? 

5.  It  has  been  demonstrated  at  a  state  experiment  station 
that  a  farm  horse  at  steady  work  should  be  fed  each  day 
1  Ib.  of  grain  and  1.2  Ib.  of  hay  for  each  100  Ib.  of  its  weight. 
If  100  ears  of  corn  make  1  bu.  (56  Ib.),  how  many  ears 
should  be  fed  per  day  to  a  work  horse  weighing  1200  Ib.  ? 
to  a  horse  weighing  1500  Ib.  ? 

6.  A  state  experiment  station  that  made  recent  tests  in 
feeding  farm  horses  reports  that  the  present  method  of 
feeding  horses  as  practiced  by  most  farmers  is  uneconomi- 
cal, as  to  the  amount  and  kind  of  grain  fed.    The  average 
loss  per  day  on  each  horse  is  placed  at  20.    What  is  the 
annual  loss  in  feeding  a  team  ? 

7.  The  department  of  agriculture  of  a  Western  state  esti- 
mates that  the  average  farm  horse  of  that  state  works  about 
1000  hr.  per  year,  and  is  fed  about  5215  Ib.  of  grain  and 
7073  Ib.  of  hay  annually.    If  the  grain  is  worth  f  0  per 
pound,  and  the  hay  %$  per  pound,  find  the  cost  of  the  horse 
labor  per  hour. 

8.  If  a  mule  doing  the  same  work  as  a  horse  can  be  fed 
for  30  less  per  day  than  the  horse,  what  is  the  annual  sav- 
ing to  a  farmer  in  using  a  mule  team  instead  of  a  horse  team? 


THE  DAIRY 
THE  DAIRY 


79 


91.  It  takes  about  8.5  Ib.  of  milk  t'o  make  1  gal.  Milk 
varies  in  the  per  cent  of  butter  fat  it  contains,  from  about 
2%  to  6%.  One  pound  of  butter  fat  will  make  about  1J  Ib. 


DAIRY  BARN  AND  SILO 

of  butter.  Much  care  should  be  used  in  the  selection  of 
milch  cows,  if  they  are  to  be  a  profitable  source  of  income 
on  the  farm. 

EXERCISE 

1.  How  many  pounds  of  butter  will  180  Ib.  of  butter  fat 
make  ? 

2.  How  many  pounds  of  butter  fat  in  290  Ib.  of  butter  ? 

3 .  If  20  per  pound  will  cover  the  expense  of  making  butter, 
which  would  be  the  more  profitable,  to  sell  butter  for  250  per 
pound,  or  the  butter  fat  to  a  creamery  at  200  per  pound  ? 

4.  If  you  live  near  a  creamery,  compare  the  prices  paid 
for  butter  fat  and  for  butter,  and  determine  which  method 
of  sale  is  the  more  profitable. 


80  STOCK  AND  FEED  PKOBLEMS 

5.  If  a  cow  averages  daily  3  gal.  of  milk  which  is  4% 
butter  fat,  how  much  butter  does  she  produce  per  year  ? 

6.  A  man  can  buy  for  $30  a  scrub  cow  that  gives  14  Ib. 
of  milk  per  day,  or  for  $70  a  Jersey  that  gives  25  Ib.  of 
milk  per  day.    If  the  scrub  cow's  milk  is  2%  butter  fat  and 
the  Jersey's  4J<%,  and  the  butter  is  worth  200  a  pound  the 
year  round,  which  cow  will  yield  the  greater  per  cent  on 
the  investment  for  a  year  ? 

7.  If  a  cow  that  gives  daily  3  gal.  of  milk  testing  4% 
butter  fat  is  fed  dry  feed  for  1\  mo.  at  $5  per  month,  and 
is  pastured  the  rest  of  the  year  at  $1.50  per  month,  what 
is  the  money  return  in  excess  of  the  cost  of  her  keep,  when 
butter  is  250  per  pound  and  skim  milk  100  per  gallon  ? 

8.  If  by  feeding  a  suitable  ration  to  a  milch  cow  she 
will  produce  10  cents'  worth  more  milk  and  butter  fat  each 
day,  what  will  the  knowledge  of  a  proper  ration  yield  a 
farmer  in  the  course  of  the  7J  feed  months  on  3  milch  cows  ? 

9.  If  it  costs  $32  a  year  to  keep  a  cow  that  produces 
200  Ib.  of  butter  fat,  what  is  the  average  cost  per  pound  of 
the  butter,  assuming  that  the  skim  milk  pays  for  all  labor  ? 

10.  A  cow  whose  milk  contains  4.2%   butter  fat  must 
produce  how  many  gallons  of  milk  to  yield  84  Ib.  of  butter  ? 

11.  Each  student  should  be  asked  to  keep  a  strict  account 
of  the  feed  given  the  cows  at  home  for  4  wk.  and  of  the 
amount  of  milk  produced,  and  estimate  at  the  local  price  of 
feed  the  cost  of  producing  1  gal.  of  milk. 

12.  A  cow  when  fed  1  bu.  of  corn  and  1  shock  of  fodder 
every  5  da.  gave  1  gal.  1  pt.  of  milk  a  day ;  when  fed  each 
day  8  Ib.  of  corn  and  3  Ib.  of  oats  crushed  together,  and  15  Ib. 
of  clover  hay,  gave  3  gal.  a  day.    If  the  cow's  milk  weighed 
8J  Ib.  to  the  gallon  and  tested  4%  butter  fat,  how  much  but- 
ter did  she  produce  in  90  da.  when  fed  on  corn  and  fodder  ? 
How  much  when  fed  on  good  rations  for  a  dairy  cow  ? 


CATTLE  AND  HOG  PEOBLEMS  81 

SILOS 

92.  Silos  are  built  with  rigid,  smooth,  perpendicular  walls, 
which  are  air-tight  to  prevent  fermentation  of  the  ensilage. 

93.  Thirty  pounds  is  the  average  weight  of  1  cu.  ft.  of 
corn  ensilage  in  a  small  silo. 

94.  One   cubic  foot  of  ensilage  per   head  is  the  usual 
daily  ration. 

EXERCISE 

1.  Assuming  that  a  cow  is  fed  daily  30  Ib.  of  ensilage  for 
a  period  of  180  da.,  what  must  be  the  capacity  in  cubic  feet 
of  a  silo  for  a  herd  of  12  ? 

2.  If  the  silo  in  problem  1  is  round,  with  a  diameter  of 
10  ft.,  what  must  be  the  height  ? 

3.  Estimating  10  tons  of  corn  and  fodder  to  the  acre,  how 
many  acres  will  be  required  to  fill  the  silo  in  problem  2  ? 

4.  How  many  tons  of  ensilage  in  a  silo  10  ft.  in  diameter 
and  29  ft.  high  ?    How  many  acres  of  corn  (10  tons  to  the 
acre)  will  it  hold  ?    How  many  cows  will  it  feed  for  180  da.  ? 

CATTLE  AND  HOG  PROBLEMS 

95.  Good  authority  places  the  weight  of  calves  at  birth 
as  follows  : 

Light-weight  calves 40-60  Ib. 

Average  calves 60-80  Ib. 

Heavy  calves .     80-110  Ib. 

96.  On  an  average  li  gal.  of  fresh  milk  will  produce  1  Ib. 
of  gain,  live  weight.    The  suckling  calf  should  gain  on  an 
average  2  Ib.  per  day.    The  fat  calf  dressed  is  from  40% 
to  50%  of  its  live  weight,  and  cattle  from  50%  to  60%  of 
their  live  weight. 

97.  Count  8£  Ib.  of  milk  to  the  gallon. 


82  STOCK  AND  FEED  PROBLEMS 

EXERCISE 

1.  Under  normal  conditions,  what  should  a  calf  weighing 
50  Ib.  at  birth  weigh  at  the  end  of  90  da.  ? 

2.  When    milk   is    worth   20$   per   gallon,  what  is  the 
cost  of  making  a  calf  that  weighs   80  Ib.  at  birth  weigh 
150  Ib.  ? 

3.  Which  is  the  better  proposition,  to  keep  a  young  calf 
for  120  da.,  feeding  it  on  an  average  2^  gal.  of  fresh  milk 
per  day,  at  12$  per  gal.,  and  then  sell  it  for  $18  ;  or  sell 
it  at  birth  for  $2  and  make  and  sell  butter  at  20$  per 
pound  from  the  milk,  which  contains  4%   butter  fat,  the 
skim  milk  and  buttermilk  paying  for  the  trouble  of  milking 
and  churning  ? 

4.  A  calf  at  birth  weighs  70  Ib. ;  at  the  end  of  60  da. 
it  weighs   220  Ib.    What  is  the  per  cent  of  gain  for  the 
period  ? 

5.  If  a  fat  calf  dressed  is  45%  of  its  live  weight,  what 
was  the  live  weight  of  a  calf  that  when  dressed  weighed 
126  Ib.  ? 

6.  If  a  beef  steer  when  dressed  is  59%  of  its  live  weight, 
what  was  the  live  weight  of  a  steer  whose  dressed  weight 
was  768£  Ib.  ? 

7.  A  steer  on  foot  weighed  1325  Ib. ;  when  dressed  it 
weighed  768^  Ib.    The  dressed  beef  was  what  per  cent  of 
its  live  weight? 

8.  According  to  the  tests  of  an  experiment  station  in 
pig  feeding,  a  pig  when  fed  for  46  da.  a  total  of  397  Ib.  of 
shelled  corn  gained  79  Ib.    At  this  rate,  how  many  pounds 
of  corn  did  it  take  to  produce  100  Ib.  of  flesh  ? 

9.  When  corn  is   50$  per  bushel  (56  Ib.  to  the  bushel), 
what  does  it  cost  to  put  1  Ib.  on  a  pig  ?    (Use  data  in 
problem  8.) 


CATTLE  ANJ)  HOG  PROBLEMS  83 

10.  At  the  time  the  test  in  problem  8  was  given,  another 
was  made  in  which  pigs  fed  for  46  da.  a  total  of  334  Ib.  of 
middlings  gained  91  Ib.    At  this  rate,  how  many  pounds  of 
middlings  would  it  take  to  produce  100  Ib.  of  flesh  ? 

11.  Is  it  cheaper  to  feed  corn  at  500  per  bushel  or  mid- 
dlings at  $1.50  per  100  Ib.  ? 

12.  If  a  hog  gains  on  an  average  11  Ib.  for  every  bushel  of 
corn  that  it  is  fed,  at  the  present  price  of  corn  and  fat  hogs 
would  it  pay  to  buy  100-pound  hogs  and  fatten  them  ? 

13.  If  1  bu.  of  corn  produces  11  Ib.  of  flesh,  when  corn 
is  500  per  bushel  what  must  be  the  price  of  fat  hogs  to 
enable  a  farmer  to   realize  500  per  bushel   for  the  corn 
when  fed  ? 

14.  Can  a  farmer  afford  to  feed  corn  at  400  per  bushel 
when  fat  hogs  are  selling  in  the  local  market  at  $5.50  per 
hundredweight  ? 

15.  If  1  bu.  of  corn  produces  11  Ib.  of  flesh,  what  is  a 
man's  profit  on  20  shotes  weighing  on  an  average  100  Ib., 
which  originally  cost  $5  each,  are  fed  corn  at  450  per  bushel 
until  they  weigh  on  an  average  257  Ib.,  and  are  then  sold  at 
$5.85  per  hundredweight? 

16.  A  lot  of  pigs  fed  in  a  yard  without  grass  made  an 
average  gain  of  100  Ib.  for  every  629  Ib.  of  corn  fed  them. 
Another  lot  of  pigs  of  the  same  stock  and  weight  were  given 
full  feed  of  corn  at  all  times  while  running  on  blue-grass 
pasture,  and  made  an  average  gain  of  100  Ib.  for  every  507  Ib. 
of  corn  fed  them.    The  pasture  made  a  saving  of  what  per 
cent  of  the  corn  ? 

17.  It  is  conservatively  estimated  that  an  acre  of  rape 
pasture  saves  2600  Ib.  of  corn  (56  Ib.  to  the  bushel)  in  the 
preparation  of  20  pigs  for  the  fattening  period.    What  is 
the  value  of  rape  when  corn  is  350  per  bushel  ? 


84  STOCK  AND  FEED  PROBLEMS 

MEAT  PROBLEMS 

98.  In  butchering  hogs  butchers  count  on  a  loss  of  25  Ib. 
on  the  first  100  Ib.,  15  Ib.  on  the  second,  and  10  Ib.  on  each 
additional  hundred.  Country-cured  meat  shrinks  one  third 
of  its  weight.  Packing  houses  employ  methods  of  curing 
meat  with  practically  no  shrinkage. 

EXERCISE 

1.  What  is  the  waste  in  butchering  a  hog  weighing  350  Ib.  ? 

2.  A  farmer  butchered  and  cut  up  a  hog  weighing  283  Ib., 
as  follows  :   head,  20  Ib. ;  backbone,  13-*  Ib. ;  spareribs,  8  Ib. ; 
feet  and  hocks,  6^  Ib. ;  lard  and  sausage,  63  Ib. ;  2  hams, 
371  Ib. ;  2  shoulders,  37  J  Ib. ;  2  sides,  43J  Ib.  Which  would 
have  been  the  more  profitable,  to  sell  the  hog  on  foot  at  the 
market  price  of  60  per  pound,  or  to  salt  and  smoke  the  salable 
meat  and  sell  it  at  the  local  price  of  country-cured  meat  ? 

3.  Is  it  better  for  a  farmer  to  sell  fresh  meat  as  follows : 
4  hams  averaging  32  Ib.  at  100  per  pound,  4  shoulders  aver- 
aging 27  Ib.  at  100  per  pound,  4  sides  averaging  28  Ib.  at 
100  per  pound;  or  to  country  cure  and  sell  the  hams  and 
shoulders  at  150  per  pound  and  the  sides  at  12-J-0  per  pound  ? 

4.  A  butcher  pays  50  a  pound  for  a  hog  weighing  139  Ib. 
It  was  butchered,  and  cut  up  as  follows :  48  Ib.  of  cutting 
meat,  at.12^0  per  pound;  9  Ib.  of  bacon,  at  100  per  pound; 
30  Ib.  of  lard,  at  100  per  pound ;  2j  Ib.  of  ribs,  at  12^0  per 
pound  ;  12  Ib.  of  head,  at  60  per  pound.   How  much  does  the 
butcher  make  ? 

5.  At  butchering  time  a  farmer  can  sell  his  hams  at  90 
per  pound.    If  one-third  is  lost  in  curing  meat,  what  price 
should  he  receive  for  the  cured  meat  that  he  may  neither 
lose  nor  gain  ? 


TRANSPORTATION 
THE  COST  OF  BAD  ROADS 

99.  Good  roads  enable  farmers  to  haul  all  their  products 
to  market  at  all  seasons  of  the  year.  The  increased  size 
of  the  load  that  can  be  hauled  and  the  less  time  required 
for  hauling  reduces  the  cost  of  marketing  crops. 


BAD  ROADS  ARE   EXPENSIVE 
EXERCISE 

1.  A  town  is  55  mi.  from  the  nearest  railroad  point.  The 
roads  are  such  that  the  average  load  hauled  is  1600  lb., 
and  the  average  time  required  for  a  round  trip  is  8  da. 
The  price  for  dray  age  from  town  to  railroad  point  is  $1  per 
hundred,  and  from  railroad  to  town  $1.50.  How  much  does 
the  freighter  receive  for  a  round  trip  when  loaded  each  way? 

85 


86 


TRANSPORTATION 


2.  If  the  road  were  piked,  the  round  trip  could  be  made 
in  4  da.  by  a  freighter  hauling  2500  Ib.  each  way.    If  the 
freighter  is  to  receive  the  same  price  per  day  for  his  work  as 
in  problem  1,  what  must  be  his  average  charge  per  hundred  ? 

3.  If  100  Ib.  of 
flour    will    last    a 
family  of  six  2  mo. 
when  eating  white 
bread  once  a  day, 
what       will       the 
freight  charges  (at 
the  rate  given   in 
problem  2)  on  the 
flour  amount  to  in 
lyr.?  What  will  be 
the  freight  charges 
if  the    family  eat 
white  bread  twice 
a  day  ? 

4.  What  amount 
would  a  good  road 
save  the  family  on 
flour   alone,   when 
the  freight  rate  is 
that  in  problem  2  ? 

5.  If  the  freight 
to  the  above  town 

is  416,000  Ib.  each  year,  what  is  the  freightage  at  $1.25  per 
hundred  ?  at  600  per  hundred  ?  What  is  the  saving  in  1  yr. 
at  the  reduced  rate  due  to  good  roads  ? 

6.  How  many  years  will  it  take  the  difference  in  freight 
rates  in  problem  5  to  build  20  mi.  of  gravel  road  at  $1800 
per  mile  ? 


THIS  HILL  MAKES  THE  FREIGHT  ON   THIS 

ROAD    TWO    CENTS    PER    MILE    FOR    EACH 

HUNDRED  POUNDS 


THE  COST  OF  BAD  ROADS 


87 


7.  A  hardware  dealer  estimates  the  life  of  a  freight  wagon 
in  continuous  service  on  the  road  described  in  problem  1 
at  1  yr.    If  it  takes  8  da.  for  a  round  trip,  how  many  miles 
of  service  are  there 

in  a  new  wagon  ? 

8.  Calling  Syr. 
the  lifetime  of  such 
a  wagon  on  a  good 
road,  when  wagons 
sell  at  $60,  what  is 
the    bad-road    tax 
paid  by  a  freighter 
in    the    course    of 
6  yr.  on  the  road  in 
problem  1  ? 

9 .  A     country 
store  on  a  gravel 
road  pays  1$  a  mile 
for    each    100   Ib. 
of   freight   hauled 
from  the   railroad 
station ;    a  county 
seat    on  the   same 
road   24  mi.   from 
the  railroad,  18  mi. 

of  which  are  not  gravel,  pays  20  a  mile  for  hauling  each 
100  Ib.  of  freight.  What  is  the  animal  bad-road  tax  paid  by 
this  county  seat  upon  300,000  Ib.  of  freight  ? 

10.  It  is  estimated  by  good  authority  that  a  certain  county 
in  Kentucky,  which  pays  annually  $70,000  for  hauling  its 
goods  from  the  railroad,  could  save  at  least  $40,000  annually 
by  having  good  roads.  What  is  the  average  bad-road  tax 
upon  each  of  the  17,789  farmers  in  the  county  ? 


ON  THIS  ROAD  FREIGHT  IS  ONE  CENT  PER 
MILE  FOR  EACH  HUNDRED  POUNDS 


88 


TRANSPORTATION 


100.  A  good  road  must  be  oval,  hard,  and  smooth.  It  is 
possible  to  make  such  a  dirt  road  by  using  the  split-log 
road  drag  illustrated  below. 


SPLIT-LOG  ROAD  DRAG 


101.  To  make  and  use  the  road  drag,  set  the  split  log 
on  edge  30  in.  apart,  with  flat  sides  to  the  front.  Fasten 
together  with  strong  hedge  or  hickory  bars,  the  ends  of 
which  are  wedged  in  2-inch  auger  holes  bored  through  the 
slabs. 

EXERCISE 

1.  Estimate  the  cost  of  making  a  road  drag  when  it  takes 
a  log  12  in.  in  diameter  and  9  ft.  long,  lumber  at  $1  per 
hundred  in  the  log,  2  drawing  chains  at  25$  each,  a  double- 
tree at  $2.50,  a  shoe  9  ft.  long  and  6  in.  wide  at  10$  per 
foot,  a  board  9  in.  wide  and  9  ft.  long  at  $1.50  per  hun- 
dred, and  the  time  required  to  make  it  1  da.  at  $1. 


THE  COST  OF  BAD  KOADS  89 

2.  A  farmer  lives  11  mi.  from  a  grain  market  in  a  county 
known  for  its  bad  roads,  on  which  1  ton  makes  a  load  for 
a  good  team.    In  an  adjoining  county,  where  the  roads  are 
graded  and  kept  smooth  and  firm  by  using  the  road  drag, 
35  cwt.  is  easily  drawn  as  a  load.    Estimate  the  bad-road  tax 
paid  by  the  farmer  living  on  the  poor  road,  who  markets 
933J  bu.  of  wheat  (60  Ib.  to  the  bushel),  for  the  hauling  of. 
which  he  pays  $2.50  per  load. 

3.  A  conservative  estimate  of  the  annual  loss  to  farmers 
because  of  bad  roads  is  750  per  acre ;  what  is  the  loss  to  a 
farmer  who  owns  80  A.  ? 

4.  If  the  annual  saving  to  the  farmers  by  maintaining 
good  roads  is  750  per  acre,  how  many  days  per  year  should 
a  farmer  work  the  roads  who  owns  120  A.  of  land,  when  a 
man  with  a  team  is  worth  $5.0.0  per  day  ? 

5.  If  a  team  can  haul  on  a  good  macadam  road  250% 
more  than  on  an  ordinary  dirt  road,  when  30  bu.  of  wheat 
makes  a  load  on  a  dirt  road,  how  many  bushels  could  be 
hauled  over  a  macadam  road? 


BUILDING  PROBLEMS 
WEATHERBOARDING 

102.  Weather-boarding  —  siding  or  clapboarding —  is  sold 
by  the  width  of  the  boards  from  which  it  is  dressed.  A  board 
6  in.  wide  can  be  dressed  into  weatherboarding  5  J  in.  wide  ; 
a  5-inch  board  can  be  dressed  into  4^-inch  weatherboarding. 


SIX-INCH   WEATHERBOARDING—  4 
1  INCH  LAP 


INCHES  EXPOSED, 


In  weatherboarding  1  in.  is  allowed  for  lap.  To  estimate  a 
bill  of  weatherboarding,  measure  the  surface  in  square  feet  ; 
to  this  add  ^  of  itself  if  6-inch  weatherboarding  is  used, 
and  f  if  5-inch  weatherboarding  is  used.  Ordinarily  no  allow- 
ance is  made  for  doors  and  windows. 

90 


SHINGLING  91 

EXERCISE 

1.  How  many  square  feet  are  there  on  one  side  of  your 
schoolhouse  ?    How  many  feet  of  6-inch  weatherboarding 
would  it  require  ?  How  many  feet  of  5-inch  weatherboarding? 

2.  How  many  feet  of  weatherboarding  would  it  take  for 
the  schoolhouse  ? 

3.  When  paying   two  men  $1.75  each  for  putting  on 
together  600  sq.  ft.  of  weatherboarding  a  day,  what  would  be 
the  carpenter's  bill  for  weatherboarding  the  schoolhouse  7 
What  would  be  the  lumber  bill  with  weatherboarding  at 
$2.75  per  hundred  ?    What  would  be  the  total  ? 

4.  When  paying  $1.50  for  each  300  ft.  of  weatherboard- 
ing placed  on  the  house,  with  $2.50  per  hundred  for  weather- 
boarding  ami  nails,  what  would  it  cost  to  weatherboard  a 
house,  having  the  dimensions  of  your  home  ? 

5 .  In  6-inch  weatherboarding  how  many  inches  are  exposed 
to  the  weather  ? 

6.  When  a  carpenter  is  estimating  the  number  of  feet  of 
weatherboarding  required  for  a  building,  why  does  he  add 
to  the  number  of  square  feet  to  be  covered  one  third  of  this 
number  when  6-inch  weatherboarding  is  used  ? 

SHINGLING 

103.  It  requires  900  shingles  that  average  4  in.  in  width, 
laid  4  in.  to  the  weather,  to  cover  100  sq.  ft.;  but  to  allow  for 
waste,  count  1000  shingles  for  100  sq.  ft. 

There  are  250  standard-size  shingles  in  a  bunch.  A  frac- 
tional part  of  a  bunch  cannot  be  bought. 

Four  bunches  of  shingles  will  cover  100  sq.  ft. 
*•  Allow  6  Ib.  of  shingle  nails  for  1000  shingles. 

Carrying  up  and  laying  6  bunches  (1500  shingles)  is  a 
day's  work  for  the  average  carpenter. 


92 


BUILDING  PROBLEMS 


EXERCISE 

1.  How  many  bunches  of  shingles  4  in.  wide  and  laid 
4  in.    to   the    weather   will   it   take    for   the   roof   of   the 
schoolhouse  ? 

2.  When   paying 
the  carpenter  $2  a 
day,   with   shingles 
at  $3  per  thousand, 
and  nails  at  30  per 
pound,      what 

will  it  cost  to 
put  a  new  roof 

SHINGLES  LAID  FOUR  INCHES  TO  THE 

on  the  school-  WEATHER 

house  ? 

3.  When  paying  a  carpenter  $1.50  per  day,  with  shingles 
at  $3.25  per  thousand,  nails  at  40  per  pound,  what  would  it 
cost  to  put  a  new  roof  on  your  home  ? 

METAL  ROOFING 

104.  Metal  roofing  is  bought  by  the  square  (100  sq.  ft.). 
Galvanized  steel  can  be  bought  at  from  $2.50  to  $4  per 
square ;  750  is  the  average  charge  for  laying.  Galvanized 
iron  can  be  bought  at  $4  per  square  ;  750  is  the  average 
charge  for  laying.  Tin  roofing  can  be  bought  at  from  $2  to 
$6  per  square ;  $1.50  is  the  average  charge  for  laying. 

EXERCISE 

1.  What  would  a  tin  roof  for  your  schoolhouse  cost  at 
$3.50  per  square  and  $1.50  per  square  for  laying  ? 

2.  Which  would  be   the  less  expensive  roof  for   your 
schoolhouse,  the  galvanized-steel  roof  at  $3.50  per  square, 
and  750  per  square  for  laying,  or  a  shingle  roof  at  $3.25  per 
thousand,  and  $1  per  square  for  laying  ? 


FLOCKING 


93 


FLOORING 

105.  A  board  2£  in.  wide,  when  tongued  and  grooved, 
covers  2  in.  of  floor  space  ;  a  board  3  in.  wide  covers  2^-  in. ; 
one  4  in.  wide  covers  3J  in.  (Some  4-in.  flooring  covers  3£  in.) 

106.  Rule.    To  estimate  a  bill  of  flooring  or  ceiling,  meas- 
ure the  square  feet  of  surface  ;  to  'this  add  £  of  itself  if 
2^-inch  flooring   is   used,    j-  of  itself  if  3-inch  flooring  is 
used,  and  -^   if  4-inch  flooring  is   used. 


EXERCISE 

1.  How  many  square  feet  of  floor  are  there  in  your  school- 
room ?    How  many  feet  of  flooring  3£  in.  wide  will  it  take  ? 

2.  How  many  feet  of  floor- 
ing 2£  in.  wide  will  be  required 
for  a  room  14  ft.  by  16  ft.  ? 

3.  What    would    it    cost    to 
floor  your  largest  room  at  home 
with  oak  flooring  2^  in.  wide  at 
$3.75  per  hundred?  with  pine 
flooring  2£  in.  wide  at  $2  per 
hundred? 


FLOORING 


4.  Estimate  the  number  of  feet  of  ceiling  4  in.  wide  it 
would  take  for  your  largest  room  at  home.    How  many  feet 
3  in.  wide  ?    (Allow  £  in.  for  tongue  and  groove.) 

5.  When  a  carpenter  is  estimating  the  number  of  feet  of 
flooring  2^  in.  wide  required  for  a  room,  why  does  he  add  to 
the  number  of  square  feet  to  be  floored  one  fourth  of  the 
number  ?    Why  does  he  add  one  fifth  of  the  number  when 
3-inch  flooring  is  used  ?  Why  does  he  add  three  thirteenths 
of  the  number  when  4-inch  flooring  is  used  ?  What  does  he 
add  when  4-inch  flooring  covers  3^  in.  ? 


94  BUILDING  PROBLEMS 

CUTTING  RAFTERS 

107.  One  half  the  width  of  a  house  (the  distance  between 
the  outside  measurements  of  the  wall  plates)  is  called  the 
run.    The  height  of  the  rafters  at  their  highest  point  above 
the  wall  plates  is  called  the  rise. 

A  roof  is  J  pitch  when  it  is  1  ft.  high  for  every  2  ft.  in 
the  width  of  the  house. 

A  roof  is  i  pitch  when  it  is  1  ft.  high  for  every  4  ft.  in 
the  width  of  the  house. 

A  roof  is  |  pitch  when  it  is  2  ft.  high  for  every  3  ft.  in 
the  width  of  the  house. 

The  parts  of  a  carpenter's  square  are  the  blade  and  the 
tongue.  The  blade  is  the  broad  and  long  part.  The  tongue 
is  the  narrow  and  short  part. 

108.  To  find  the  length  of  rafters,  (1)  measure  the  width 
of  the  house  (distance  between  the  outside  measurements 
of  the  rafter  plates) ;  (2) 

decide  on  the  rise   of  the 

rafters ;  (3)  counting  a  foot     P<*>*<f  ^ 

an  inch  on  the  square,  take 

J  the  width  of  the  house  on 

the  blade;  (4)  take  the  rise  RMINING  THE  ^Gm  OF  A 

on  the  tongue;    (5)   place  RAFTER 

the  square  with  these  two 

points  on  a  straight  line  or  the  straight  edge  of  a  board  and 

mark  the  points ;  (6)  then  measure  the  distance  between  the 

points  for  the  length  of  the  rafters. 

EXAMPLE.  A  house  18  ft.  wide  is  to  have  a  roof  J  pitch ;  that 
is,  the  roof  is  to  be  1  ft.  in  height  for  every  3  ft.  in  the  width  of  the 
house.  Letting  an  inch  on  the  square  represent  a  foot,  take  on  the 
blade  of  the  square  J  the  width  of  the  house  (9  in.),  on  the  tongue 
take  J  the  width  of  the  house. 

The  length  of  the  rafter  without  a  projection  over  the  side  of  the 
house  is  the  distance  between  9  on  the  blade  and  6  on  the  tongue. 


CUTTING  EAFTEES  95 

EXERCISE 

1.  What  length  must  rafters,  without  a  projection,  be  cut 
for  a  shed  12  ft.  wide,  the  roof  to  be  1  pitch  ? 

2.  What  length  must  rafters,  without  a  projection,  be  cut 
for  a  shed  12  ft.  wide,  the  roof  to  be  ^  pitch  ? 

3.  What  length  must  rafters,  without  a  projection,  be  cut 
for  a  roof  9  ft.  wide,  the  roof  to  be  §  pitch  ? 

109.  To  cut  a  rafter  pattern,  without  a  projection,  out  of  a 
2  by  4  scantling,  (1)  lay  off  the  length  of  the  rafter  on  one 
of  the  straight  edges  of  the  scantling ;  (2)  place  the  tongue 
of  the  square  with  the  point  of  the  rise  on  the  upper  mark, 
with  the  point  of  run  (on  the  blade)  upon  the  same  edge  of  the 


Point  of  Run 
RAFTER  PATTERN  WITHOUT  PROJECTION  FOR  EAVES 

scantling ;  (3)  mark  the  position  of  the  tongue  of  the  square 
for  the  upper  cut ;  (4)  next  place  the  point  of  the  run  (on  the 
blade)  on  the  lower  mark,  with  the  point  of  the  rise  (on 
the  tongue)  upon  the  same  edge  of  the  scantling ;  (5)  mark 
the  position  of  the  blade  for  the  lower  cut. 

110.  To  cut  a  rafter  pattern,  with  a  projection  for  eaves, 
from  a  2  by  4  scantling,  (1)  draw  a  straight  line  along 
the  middle  of  the  broad  side  of  the  scantling;  (2)  on  this 
line  lay  off  the  length  of  the  rafter  without  the  projection ; 
(3)  place  the  tongue  of  the  square  with  the  point  of  the 
rise  on  the  upper  mark,  with  the  point  of  the  run  (on  the 
blade)  upon  the  line ;  (4)  mark  the  position  of  the  tongue 


96  BUILDING  PEOBLEMS 

of  the  square  for  the  upper  cut ;  (5)  next  place  the  point  of 
the  run  (on  the  blade)  on  the  lower  mark  with  the  point  of 
the  rise  (on  the  tongue)  upon  the  line ;  (6)  mark  the  posi- 
tion of  the  blade  for  the  lower  cut ;  (7)  before  removing  the 


Watt  Plate  Cut\ 


RAFTER  PATTERN  WITH  PROJECTION  FOR  EAVES 

square  from  this  position,  erect  a  perpendicular  to  the  square 
at  the  point  of  the  run  (on  the  blade)  for  the  cut  that  fits 
against  the  outside  of  the  roof  plate ;  (8)  if  the  projection  is 
to  be  1  ft.,  saw  off  the  rafter  1  ft.  below  this  mark. 

EXERCISE 

1.  Lay  off  on  a  board  the  pattern  of  a  rafter  for  a  house 
18  ft.  wide,  ^  pitch,  the  projection  of  each  rafter  being  1  ft. 

2.  Lay  off  on  a  board  the  pattern  of  a  rafter  for  a  coal  shed 
8  ft.  wide,  i  pitch,  the  projection  of  each  rafter  being  9  in. 

3.  Lay  off  on  a  board  the  pattern  of  a  rafter  for  a  wagon 
shed  10  ft.  wide,  J  pitch,  the  projection  being  9  in. 

4.  Estimate  the  lumber  bill  for  the  house  on  page  97,  the 
rough  stock  being  as  follows :  studding,  167  pieces,  2  in.  by 
4  in.,  12  ft.  long ;  sills,  16  pieces,  2  in.  by  8  in.,  16  ft.  long ; 
girders,  12  pieces,  2  in.  by  8  in.,  16  ft.  long ;  floor  joists,  40 
pieces,  2  in.  by  8  in.,  10  ft.  long ;  floor  joists,  20  pieces,  2  in. 
by  8  in.,  12  ft.  long;  ceiling  joists,  40  pieces,  2  in.  by  6  in., 
16  ft.  long ;  weatherboarding,  6-inch  width ;  ceiling,  3j-mch 
width ;  floors,  3^-inch  width ;  brick  for  2  one-stove  flues, 


STONEWORK  AND  BRICKWORK 


97 


14  ft.  high ;  hip  rafters,  4  pieces,  2  in.  by  8  in.,  24  ft.  long ; 
common  rafters,  4  pieces,  2  in.  by  6  in.,  18  ft.  long;  jack 
rafters,  2  in.  by  6  in.,  450  ft.  total  length ;  sheeting,  450  ft. ; 
bunches  of  shingles  (1100  sq.  ft.  in  roof). 

5.  Estimate  at  market  prices  the  cost  of  the  bill  of  lum- 
ber in  problem  4. 

STONEWORK  AND  BRICKWORK 

111.  Stonework  is  estimated,* by  the  cubic  yard  or  the 
running  perch.  Stone  in  the  quarry  or  in  massive  buildings 
is  measured  by  the  cubic  yard.  Rubble  work,  or  the  founda- 
tion of  the  average  house,  is  measured  by  the  running  perch. 


A  ONE-ROOM  RURAL  SCHOOLHOUSE 

A  running  perch  is  a  stone  wall,  or  fence,  38  ft.  long  and 
1  ft.  high,  regardless  of  the  thickness. 

Brickwork  is  estimated  by  the  1000. 

112.  Builders  do  not  follow  any  uniform  Tule  in  estimat- 
ing the  number  of  bricks  required  for  a  wall.  A  well-known 


BUILDING  PROBLEMS 


contractor  counts  16  bricks  of  the  ordinary  size  (8"x4"x2") 
for  every  square  foot  of  surface  in  a  wall  8  in.  thick  ;  24  for 
a  wall  12  in.  thick.  He  makes  a  deduction  for  half  of  the 
space  of  all  openings. 


Aisle    18  Inches  Wide 


Class  Room  21  Ft.  X  30  Ft. 


All  Windows  3  Ft.  X  6  Ft.  6  In. 


Row  (f  Desks  3  Ft.  Wide 


_££2<2 


JU 


FLOOR  PLAN  OF  SCHOOLHOUSE 

113.  Rule.  To  estimate  the  bricks  for  a  wall,  multiply  the 
distance  around  the  building  by  the  height  of  the  building 
in  feet  and  make  a  deduction  for  half  of  the  openings  in 
square  feet ;  multiply  this  product  by  16  if  the  wall  is  8  in. 
thick,  and  by  24  if  the  wall  is  12  in.  thick. 


STONEWOEK  AKD  BEICKWOEK 


EXERCISE 


99 


1.  How  many  running  perches  of  stone  are  there  in  a 
rock  fence  80  rd.  long  and  4i  ft.  high  ? 

2 .  How  many  running  perches  of  stone  are  there  in  the  foun- 
dation of  a  house  24  ft.  by  28  ft.,  if  the  foundation  is  3  ft.  high  ? 

3.  How  many  cubic  yards  of  dirt  are  removed  in  exca- 
vating for  a  cellar  30  ft.  long,  30  ft.  wide,  and  6  ft.  deep  ? 


ROOF  PLAN 

4.  Estimate  the  cost  of  a  brick  wall  for  a  house  30  ft.  long, 
26  ft.  wide,  16  ft.  high,  and  8  in.  thick,  when  bricks  are 
worth  $12  per  thousand. 

5.  To  lay  800  bricks  is  a  fair  day's  work  for  a  good  brick- 
layer.   How  much  will  he  receive  at  $4  per  day  for  building 
the  walls  in  the  above  problem  ? 

6.  Measure  the  schoolhouse  and  estimate  the  number  of 
bricks  it  would  take  to  make  brick  walls  8  in.  thick.    How 
many  rubbles  of  stone  would  it  take  for  the  foundation  ? 


100 


BUILDING  PROBLEMS 


7.  Estimate  how  many  rubbles  of  stone  there  are  in  the 
foundation  of  your  home. 


RUBBLE  WORK 

114.  Bricks  are  usually  8  in.  long,  4  in.  wide,  and  2  in. 
thick,  and  average  in  weight  5  Ib. 

115.  A  flue  for  one  stove  is  8  in.  by  8  in.  in  the  clear.    It 
takes  6  bricks  for  the  round  and  4  rounds  to  build  1  ft.  high. 

A  flue  for  two  stoves  is  12  in.  by  8  in.  in  the  clear.    It 
takes  7  bricks  for  a  round  and  4  rounds  to  build  1  ft.  high. 

EXERCISE 

1.  How  many  bricks  will  it  take  for  a  10-foot  flue  for 
one  stove  ? 

2.  How  many  bricks  will  it  take  for  a  14-foot  flue  for 
one  stove  ? 


3.  How  many  bricks  can  be  placed  in  a  wagon  bed  10  ft. 
long,  3  ft.  wide,  and  12  in.  deep  ?  What  is  the  weight  of 
the  load? 


PAINTING  101 

4.  How  many  bricks  will  it  take  for  a  22-foot  flue  for  two 
stoves  ? 

5.  With  brick  at  $10  per  thousand,  what  will  the  brick 
cost  for  a  flue  12  in.  by  8  in.  in  the  clear,  and  27  ft.  high  ? 

6.  How  many  trips  must  the  wagon  make  to  the  brick- 
yard, to  haul  the  brick  in  problem  5  ?  !  I  \  J  I  \  » 

PAINTING 

116.  Allow  1  gal.  of  paint  to  every  250  sq.  ft. 
A  thousand  square  feet  is  considered  a  fair  day's  work 
for  a  painter. 

EXERCISE 

1.  How  many  gallons  of  paint  would  it  take  for  one  coat 
for  the  walls  and  ceiling  of  the  schoolroom  ? 

2.  What  would  it  cost  to  give  the  outside  of  the  school- 
house  two  coats  of  paint,  with  paint  at  $1.90  per  gallon? 

3.  When  a  painter  charges  $2.50  per  day,  and  paint  is 
$1.90  per  gallon,  what  will  be  the  cost  of  two  coats  of  paint 
for  the  outside  of  your  home  ? 

4.  If  you  do  the  work  yourself,  with  paint  at  $1.60  per 
gallon,  what  will  it  cost  to  paint  a  floor  16  ft.  by  14  ft.  ? 


MACHINE,  SHOP,  AND  DRAFT  PROBLEMS 
v      i:a*V"  SHOP  PROBLEMS 

117.  Harses'Koes  average  1  Ib.  each  at  4^0  per  pound ; 
nails  average  112  to  the  pound,  at  150  per  pound. 

EXERCISE 

1.  When  a  blacksmith  furnishes  shoes  and  nails,  and 
shoes  a  horse  all  round  for  800,  what  does  he  receive  for 
his  labor  and  the  use  of  his  tools  ?  When  he  charges  $1.60  ? 

2.  Inquire  of  your  father  how  many  shoes  a  work  horse 
will  wear  during  a  year  and  what  the  price  of  shoeing  is. 
Then  estimate  what  it  costs  him  to  keep  his  horses  shod  for 
a  year. 

3.  Iron  that  weighs  6.8  Ib.  per  foot  is  used  in  making 
a  set  of  tires  for  a  wagon  whose  fore  wheels  are  42  in. 
in  diameter,  the  rear  wheels  46  in.  in  diameter.    At  40  per 
pound,  what  will  the  iron  cost  for  a  set  of  tires  ? 

4.  What  will  be  the  cost  of  the  leather  to  cover  the  seat 
of  a  chair  13  in.  in  diameter,  if  the  leather  is  bought  in  a 
square  at  500  per  square  foot? 

5.  I  can  get  a  pair  of  shoes  half-soled  for  900.    If  it  takes 
12  oz.  of  leather  valued  at  500  per  pound  and  20  worth  of 
tacks  to  do  the  job,  how  much  do  I  save  by  doing  the  work 
myself  ? 

6.  A  screw  has  13  threads  to  the  inch.    How  many  turns 
will  it  take  to  move  it  2|-  in.  ? 

102 


PEOBLEMS  WITH  THE  LEVER  103 

PROBLEMS  WITH  THE  LEVER 

118.  The  seesaw  board  is  one  kind  of  lever ;  the  point  of 
support  is  called  the  fulcrum. 

119.  The  seesaw  board  will  balance  when  the  weight  on 
one  end  multiplied  by  its  distance  from  the  fulcrum  equals 
the  product  of  the  weight  on  the  other  end  by  its  distance 
from  the  fulcrum. 

EXERCISE 

1.  John  weighs  100  Ib.  and  sits  5  ft.  from  the  fulcrum ; 
where  must  Oscar,  who  weighs  80  Ib.,  sit,  to  make  the  see- 
saw board  balance  ? 

2.  Cyrus,  who  weighs  120  Ib.,  sits  on  a  seesaw  6  ft.  from 
the  fulcrum ;  his  sister,  who  weighs  60  Ib.,  sits  4  ft.  from 
the  fulcrum  on  the  same  side.    Their  father  sits  on  the  other 
end  of  the  board  5  ft.  4  in.  from  the  fulcrum.    How  much 
does  their  father  weigh  if  the  seesaw  balances  ? 


100   Lb.X6        =====  12  X    50 


jc 6in.—  -- 12  in. 

LEVER 

3.  A  man  with  a  crowbar  6  ft.  long  places  one  end  of  it 
under  a  stone  1  ft.  from  the  fulcrum.    If  he  weighs  180  Ib., 
how  many  pounds  of  the  stone  can  he  lift  ? 

4.  A  horse  hitched  to  a  doubletree,  18  in.  from  the  clevis 
that  attaches  it  to  a  plow,  exerts  a  pull  of  150  Ib.    Another 
horse  hitched  to  the  other  end  of  the  doubletree,  20  in.  from 
the  clevis,  exerts  a  pull  of  how  many  pounds  if  both  horses 
pull  evenly  ? 

5.  A  team  is  hitched  to  a  doubletree  4  ft.  long.    At  what 
point  must  the  doubletree  be  attached  to  a  plow  so  that  one 
horse  will  pull  twice  as  much  as  the  other  ? 


104    MACHINE,  SHOP,  AND  DRAFT  PROBLEMS 

6.  A  team  is  hitched  to  a  doubletree  4  ft.  long.  At  what 
point  must  the  doubletree  be  attached  to  a  load  so  that  one 
horse  will  pull  1^  times  as  much  as  the  other  ? 


DOUBLETREE  EVENER 

7 .  When  the  draft  is  6  Ib.  per  square  inch  of  cross  section 
of  the  furrow,  estimate  the  draft  of  a  12-inch  plow  running 
6  in.  deep ;  of  a  14-inch  plow  running  6  in.  deep. 

NOTE.  In  general,  the  horse  is  able  to  exert  a  pull  equal  to  ^ 
or  J  of  his  weight.  A  plow  will  generally  require  a  pull,  or  draft, 
of  from  4  to  8  Ib.  per  square  inch  of  cross  section  of  the  furrow. 

8.  How  many  square  inches  are  there  in  the  cross  section 
of  a  furrow  12  in.  wide  and  4  in.  deep  ?    What  pull  does  a 
team  exert  in  plowing  if  the  draft  is  5  Ib.  per  square  inch  ? 


CROSS  SECTION  OF  A  FURROW 


9.  A  team  weighing  2500  Ib.  is  to  be  used  in  plowing  a 
field  5  in.  deep.  If  the  team  exerts  a  pull  of  £  of  its  weight, 
and  the  draft  is  4  Ib.  per  square  inch  of  cross  section  of  the 
furrow,  should  a  12-inch  or  a  14-inch  plow  be  used  ? 


GEKEEAL  PROBLEMS  105 

GENERAL  PROBLEMS 

120.  It  is  possible  to  plan  work  on  the  farm  when  the 
rate  at  which  it  is  done  is  definitely  known. 

1.  In  practical  demonstration  it  has  been  shown  that  a 
horse  at  his  best  for  drawing  a  heavy  load  moves  at  the  rate 
of  2.9£ ft.  per  second.    How  many  miles  is  this  per  hour? 

2.  It  is  estimated  that  a  good  horse  carrying  160  Ib. 
should  be  able  to  trot  7  ft.  per  second  7  hr.  a  day.   How  many 
miles  will  he  trot  in  a  day  ? 

3 .  If  a  man  drives  from  his  home  to  town  in  3  hr.  at  the  rate 
of  4.1  ft.  per  second  for  J  of  the  time,  and  8.2  ft.  per  second 
for  the  rest  of  the  time,  what  is  the  distance  to  the  town  ? 

4.  If  9  hr.  is  the  actual  time  per  day  that  a  team  draws  a 
self-binder,  and  if  the  binder  cuts  a  6-foot  strip,  what  is  the  * 
speed  of  the  horses  per  hour  if  14  A.  is  a  day's  work  ? 

5.  If  a  breaking  plow  turns  a  strip  12  in.  wide,  how 
many  furrows  80  rd.  long  are  turned  in  plowing  1  A.  ? 

6.  How  many  miles  does  a  team  walk  in  breaking  1  A. 
(55  rd.  by  2  j£  rd.)  with  a  12-inch  plow  ?  with  a  16-inch  plow? 

7.  If  a  team  travels  16£  mi.  a  day  with  a  breaking  plow, 
how  many  days'  work  can  a  man  save  in  plowing  30  A.  (110  rd. 
by  43T7T  rd.)  by  using  a  16-inch  instead  of  a  12-inch  plow  ? 

8.  If  a  grain  binder  cuts  a  strip  6  ft.  wide,  how  many 
acres  of  wheat  will  it  cut  in  traveling  11  mi.  ? 

9.  Calling  16£  mi.  an  average  day's  work,  how  many 
acres  a  day  will  a  binder  cover  that  cuts  a  6-foot  strip  ? 

10.  How  many  miles  does  a  team  walk  in  harrowing  a  field 
80  rd.  by  40  rd.  with  a  10-foot  harrow  ? 

11.  When  a  man  can  cut  12  A.  of  grass  per  day,  how 
many  acres  must  he  cut  that  he  may  rake  it  the  same  day, 
if  he  rakes  twice  as  fast  as  he  cuts  ? 


BUSINESS  PROBLEMS 
BORROWING  MONEY  FROM  INDIVIDUALS 

121.  Individuals,  as  a  rule,  demand  the  interest  when  a 
note  is  due,  or  annually,  if  the  note  runs  longer  than  a  year. 
They  reckon  interest  by  months  and  years,  and  may  or  may 
not  require  the  maker  of  the  note  to  give  security. 

122.  A  note  is  a  written  promise  to  pay  a  certain  sum  of 
money  at  a  specified  time. 

The  following  is  the  usual  form  of  a  note : 

Booneville,  Ky.,  March  1, 1913 

One  year  after  date  I  promise  to  pay  to  Raymond  David- 
son or  order,  Eighty-five  Dollars,  for  value  received,  with 
interest  at  6%.  Silas  Moore 

NOTE  TO  TEACHER.  Require  each  member  of  the  class  to  give  his 
note  to  a  classmate.  Continue  this  drill  until  note  writing  becomes  a 
simple  matter. 

INTEREST 

123.  Interest  is  money  paid  for  the  use  of  money,  and  is 
reckoned  by  the  year. 

124.  Rule.    To  find  the  interest  on  the  face  of  a  note, 
multiply  the  face  of  the  note  ly  the  rate  of  interest  expressed 
as  hundredths;  then  multiply  by  the  number  of  years,  or  the 
fractional  part  of  a  year,  that  the  note  runs. 

EXAMPLE.    What  is  the  interest  on  f 200  for  1  yr.  6  mo.  at  6%  ? 
SOLUTION.  |200  (Principal) 

.06  (Rate) 
$12.00 

1^     (Years)  1  yr.  6  mo.  =  \\  yr. 
$18.00  (Interest) 

106 


USING  THE  BANK  107 

EXERCISE 
Find  the  interest  on: 

1.  $500  for  3  yr.  at  6%.         4.  $125  for  9  yr.  at  6%. 

2.  $50forlyr.6mo.at6%.     5.  $160  for  6  yr.  at  8%. 

3.  $75  for  6  yr.  at  6%.  6.  $250  f or  1  y r.  3  mo.  at  7 % . 

USING  THE  BANK 

125.  The  first  step  to  be  taken  in  opening  an  account  with 
a  bank  is  to  deposit  some  money,  and  receive  a  pass  book  in 
which  all  deposits  are  entered  as  credits.    This  book  belongs 
to  the  customer,  and  should  be  left  with  the  bank  monthly 
to  be  balanced.    It  is  then  returned  to  the  owner  with  all 
canceled  checks. 

It  is  the  customer's  duty  to  examine  carefully  the  account 
of  all  checks,  and  report  to  the  bank  at  once  for  correction 
any  possible  mistake. 

CHECKS 

126.  A  check  is  an  order  for  a  bank  to  pay  a  certain  sum 
of  money  to  the  person  designated,  or  to  his  order,  out  of 
the  deposit  of  the  person  who  signs  the  check. 


No.  /  HYDEX,  KY.,  $un&  3,  19/c? 

HYDEN  CITIZENS'  BANK 

Pay  to  the  order  of 

@Ae^t£A,  MKOK f/0.- 


108  BUSINESS  PROBLEMS 

127.  A  check  should  be  endorsed  on  the  back  before  it  is 
cashed.    An  endorsement  is   simply  the  signature  of  the 
owner  of  the  check  on  the  back  of  it. 

Where  is  the  money  deposited  with  which  this  check  is  to 
be  paid  ? 

Who  gets  the  money  on  this  check  ? 

Who  pays  the  check  ? 

Whose  name  should  appear  on  the  back  of  the  check  when 
it  is  cashed  ? 

CERTIFIED  CHECKS 

128.  When  away  from  home  among  strangers,  or  when 
sending  a  check  to  strangers,  it  is  wise  to  use  a  certified 
check,  to  make  certain  that  your  check  will  be  promptly 
honored  or  paid. 


No.  17  HYDEN,  KY.,  Way  /, 

HYDEN  CITIZENS'  BANK 

Pay  to  the  order  of 


Dollars 
For  S 

/if. 


A  certified  check  is  one  the  payment  of  which  is  guaran- 
teed by  the  bank  on  which  it  is  drawn. 

BORROWING  FROM  BANKS 

129.  Banks  demand  the  interest  on  a  note  to  be  paid  in 
advance,  the  maker  of  the  note  to  give  security ;  and,  for 
the  most  part,  they  compute  the  interest  for  the  exact 
number  of  days. 


BOEKOWING  FROM  BANKS  109 

130.  A  common  form  of  a  bank  note  is  here  shown : 


BEREA,  KY.,  ^aw,.  /,  197  3 

,  1A}~&  promise  to  pay  to  the  order  of 
Cbc  Bcrca  JVational  Bank,  Berea,  Ky. 


Negotiable  and  payable  at  THE  BEREA  NATIONAL  BANK,  Berea, 
Ky.,  value  received,  with  interest  at  the  rate  of  6  per  centum 
per  annum  after  maturity  until  paid.  Indorsers  waive  demand, 
protest,  and  all  legal  diligence  to  collect. 


The  day  this  note  was  made,  Mr.  Hacker  paid  to  the 
bank  $15,  the  interest  for  6  mo.;  that  is,  he  received  from 
the  bank  $485.  The  interest  is  called  bank  discount;  the 
amount  received  by  the  maker  of  the  note  is  called  the 
proceeds. 

The  note  is  due  in  6  calendar  months.  On  July  1,  1913, 
Mr.  Hacker  will  pay  the  bank  $500,  or  he  will  renew  the 
note,  paying  the  interest  in  advance. 

EXERCISE 

1.  Let  each  member  of  the  class  write  a  note  for  $200  for 
6  calendar  months,  with  interest  at  6%,  payable  to  the  local 
bank.  Some  members  of  the  class  or  school  may  sign  the 
note  with  the  maker  for  security.  When  is  this  note  due  ? 
What  is  the  bank  discount  ?  What  are  the  proceeds  of  the 
note? 


110  BUSINESS  PROBLEMS 

2.  Let  each  member  of  the  class  write  a  note  for  $200  for 
60  da.,  with  interest  at  6%,  payable  to  the  local  bank. 
Secure  some  member  of  the  class  for  security.  When  is  the 
note  due  ?  What  is  the  bank  discount  ?  What  are  the 
proceeds  of  the  note  ? 

i 

THE  Six  PER  CENT  METHOD  OF  FINDING  INTEREST 

131.  The  interest  on  $1  for 

1  yr.  is  $0.06  (60) 

2  mo.  is  $0.01 
1  mo.  is  $0.005 

30  da.  (1  mo.)  is  $0.005 
6  da.  is  $0.001  (1  mill) 

When  the  rate  is  6%,  count  ^  of  the  months  cents  and 
£  of  the  days  mills,  and  multiply  their  sum  by  a  number 
equal  to  the  number  of  dollars  in  the  principal. 

EXAMPLE.   Find  the  interest  on  $870  for  3  mo.  12  da.  at  6%. 

SOLUTION.    J  of  months  counted  as  cents.  2) 3  mo.  =  $0.015 

J  of  days  counted  as  mills,  6)l2         =    0.002 

$0.017 

The  interest  on  $1  for  3  mo.  12  da.  at  6%  is 
$0.017,  and  on  $870  it  would  be  870  x  $0.017  =  $14.79. 

132.  If  the  rate  is  any  other  than  6%,  find  the  interest 
on  $1  for  the  given  time  at  6%,  and  take  of  this  sum  the 
fractional  part  the  given  rate  is  of  6%  and  multiply  by  a 
number  equal  to  the  number  of  dollars  in  the  principal. 

EXAMPLE.    Find  the  interest  on  $600  for  5  mo.  18  da.  at  7%. 

SOLUTION.    £  of  months  counted  as  cents,  $0.025 

^  of  days  counted  as  mills,  0.003 

$0.028 

7%  the  rate  =  J  of  $0.028  =  $0.032f . 
600  x  $0.032§  =  $19.60. 


BORROWING  FKOM  BANKS  111 

EXERCISE 

Find  the  discount  on : 

1.  $875  for  10  mo.  9  da.  at  6%. 

2.  $350  for  7  mo.  15  da.  at  6%. 

3.  $890  for  9  mo.  24  da.  at  6%. 

4.  $370  for  2  mo.  13  da.  at  6%. 

5.  $365  for  19  da.  at  6%. 

6.  $135  for  15  mo.  12  da.  at  6%. 

7.  $550  for  1  yr.  4  mo.  6  da.  at  6%. 

8.  $1000  for  4  mo.  18  da.  at  7%. 

9.  $1200  for  3  mo.  at  8%. 

10.  $860  for  1  mo.  17  da.  at  8%. 

11.  $760  for  1  mo.  19  da.  at  5%. 

12.  $980  for  5  mo.  8  da.  at  7%. 

THE  DAY  METHOD  OF  FINDING  INTEREST 

133.  In  the  Six  Per  Cent  Method  of  Finding  Interest  it 
was  seen  that  one  mill,  or  .001  of  a  dollar,  was  the  interest 
on  $1  for  6  da.  at  6%.  Then  the  interest  on  any  principal 
at  6%  for  any  number  of  days  may  be  found  by  moving 
the  decimal  point  in  the  principal  three  places  to  the  left 
and  multiplying  by  the  number  of  days  and  dividing  thu$ 
result  by  6. 

EXAMPLE.   Find  the  interest  on  $350  for  48  da.  at  6%. 

SOLUTION.  Moving  the  decimal  point  three  places  to  the  left  in 
the  principal,  we  have  $0.350.  Multiplying  this  by  48  gives  $16.80 
Dividing  this  result  by  6  gives  $2.80. 


112 


BUSINESS  PEOBLEMS 


EXERCISE 


1.  Reducing  the  time  expressed  in  months  to  days,  using 
the  Day  Method,  find  the  interest  at  6%  on  the  following : 


Principal 

Time 

Principal 

Time 

$800 
75 

60  da. 
90  da. 

$385.00 
305.50 

2  mo.    5  da. 
1  mo.    7  da. 

135 

75  da. 

85.50 

89  da. 

186 

24  da. 

100.75 

60  da. 

786 

2  mo.  10  da. 

135.65 

33  da. 

1600 

4  mo.  19  da. 

127.25 

85  da. 

1855 

1  mo.    3  da. 

134.16 

3  mo.  17  da. 

2.  The  following  notes  were  made  to  the  Berea  Bank  & 
Trust  Co.,  Berea,  Ky.  Find  the  date  when  they  are  due. 
Using  the  Six  Per  Cent  Method,  find  the  bank  discount  and 
the  proceeds. 


Date  of  note 

Time 

Face 

Rate  of 
discount 

1.  May  20  1913  

4  mo. 

$150 

6% 

2.  May  20,  1913  

90  da. 

200 

6% 

3    July  1   1913 

6  mo. 

450 

n 

4.  August  19,  1913  .... 
5.  September  2,  1913  .    .    . 

30  da. 
96  da. 

800 
750 

6% 
6% 

134.  Since  banks  take  the  interest  in  advance,  the  maker 
of  a  note  in  order  to  realize  a  definite  sum  of  money  must 
give  his  note  for  a  larger  amount  of  money  than  the  sum  to 
be  realized. 

EXAMPLE.  For  what  sum  must  I  give  my  note  to  a  bank  for  60  da., 
with  interest  at  6%,  that  I  may  receive  from  the  bank  $99  ? 

SOLUTION.  Since  banks  take  the  interest  in  advance,  the  interest 
on  each  $1  borrowed  for  60  da.  at  6%,  which  is  1<£,  is  taken  out  of 
every  dollar.  Thus,  the  borrower  realizes  only  99<£  on  each  dollar  on 


DISCOUNTING  NOTES  113 

the  face  of  the  note.  Therefore,  for  every  $0.99  the  maker  of  the  note 
receives  from  the  bank,  he  must  give  his  note  for  $1 ;  then  to  re- 
ceive $99  he  must  make  his  note  for  as  many  dollars  as  $0.99  is 
contained  times  in  $99,  the  proceeds  of  the  note.  The  face  of  the 
note  is  $100. 

EXERCISE 

1.  For  what  sum  must  I  give  my  note,  payable  to  a  bank, 
for  6  mo.  with  interest  at  6%,  so  that  I  may  realize  $291? 

2.  For  what  sum  must  I  give  my  note,  payable  to  a  bank 
in  60  da.,  with  interest  at  6%,  so  that  I  may  realize  $495  ? 

3.  For  what  sum  must  I  give  my  note,  discounted  at  a 
bank,  for  45  da.  at  6%,  to  realize  $394  ? 

DISCOUNTING  NOTES 

135.  Agents  and  business  men  usually  take  notes  from 
their  customers  due  at  a  future  date.  If  they  need  the 
money  before  the  notes  become  due,  they  sell  them  to  a 
bank.  When  a  bank  buys  a  note,  it  is  said  to  discount  the  note. 

The  bank  buys  the  note  and  the  interest  due  at  maturity, 
and  discounts  the  amount  of  the  note  at  maturity  for  the 
exact  number  of  days  of  the  period  of  discount. 

EXAMPLE.   $500.  HAZARD,  KY.,  May  14,  1913 

Three  months  after  date,  for  value  received,  I  promise  to  pay 
James  H.  Tate,  or  order,  Five  Hundred  Dollars,  with  interest  at  6%. 

ROBERT  C.  PORTER 

On  May  25,  1913,  Mr.  Tate  sold  this  note  to  the  Perry  County 
State  Bank  at  Hazard,  Ky.  The  time  the  note  is  to  run  is  expressed 
in  months,  so  the  date  of  maturity  will  be  three  calendar  months 
from  the  date  on  which  the  note  was  made,  or  August  14,  1913. 

Banks  reckon  the  terms  of  discount  by  counting  the  actual  number 
of  days  from  the  date  of  discount  to  the  date  of  maturity.  There  are 
81  da.  of  discount  from  May  25  to  August  14. 

SOLUTION.  Interest  on  $500  for  3  mo.  at  6%  =  $7.50.  Value  of 
note  at  maturity  =  $500  +  $7.50  =  $507.50.  Discount  on  $507.50  foi 
81  da.  at  6%  =  $6.85.  Mr.  Tate  received  from  the  sale  of  this  note 
$507.50  -  $6.85  =  $500,65. 


114  BUSINESS  PROBLEMS 

EXERCISE 

1.  Mr.  Summers  discounted  the  following  note  at  the 
Greene  Co.  National  Bank  at  Greeneville,  Tenn.,  Novem- 
ber 1,  1913,  at  6%.    What  did  he  realize  on  the  sale? 

$850.  TUSCULUM,  TENN.,  Oct.  6,  1913 

Sixty  days  after  date,  for  value  received,  I  promise  to  pay 
Joseph  Summers,  or  order,  Eight  Hundred  Fifty  Dollars, 
with  interest  at  6%.  CAEL  w  LQWEY 

2.  Mr.  Rudder  discounted  the  following  note  at  the  Lon- 
don National  Bank  at  London,  Ky.,  April  12,  1913,  at  6%. 
What  did  he  realize  on  the  sale  ? 

$235.  LONDON,  KY.,  Jan.  8,  1913 

Four  months  after  date,  for  value  received.  I  promise  to 
pay  Roscoe  Eudder,  or  order,  Two  Hundred  Thirty-five 
Dollars,  with  interest  at  6%.  JoE  E  ElDDLE 

PAYING  CASH  FOR  GOODS 

136.  Paying  cash  for  goods  should  enable  the  purchaser 
to  buy  his  goods  cheaper  —  first,  because  the  merchant  has 
his  cash  to  use  in  business  or  to  put  at  interest ;  second, 
because  the  merchant  who  sells  for  cash  only  has  110  bad 
debts  to  lose  ;  third,  because  the  merchant  who  does  a  credit 
business  collects  his  bad  debts  from  those  who  pay  their  bills. 

EXAMPLE.  A  farmer  bought  goods  at  a  credit  store  to  the  amount 
of  $77.25  on  6  mo.  time.  What  was  the  cash  value  of  the  goods,  money 
being  worth  6%  ? 

SOLUTION.  $1  at  6%  for  6  mo.  will  amount  to  $1.03.  Thus,  a  debt 
of  $1.03  due  in  6  mo.  is  worth  at  present  only  $1.  Then  the  cash  value 
of  $77.25  due  in  6  mo.  without  interest  is  worth  as  much  as  $1.03  is 
contained  times  in  $77.25.  The  cash  value  is  $75. 


STATE  AND  LOCAL  TAXES  115 

EXERCISE 

1.  I  bought  at  a  credit  store  goods  to  the  amount  of 
$55.08  for  4  mo.    How  much  ready  cash  will  be  required  to 
pay  the  bill,  money  being  worth  6%  ? 

2.  I  bought  at  a  credit  store  goods  to  the  amount  of 
$101.50  for  3  mo.    A  neighbor  bought  the  same  bill  of  goods, 
paying  cash.   What  was  his  loss,  money  being  worth  6%  ? 

3.  A  farmer  sold  a  horse  for  $175  on  6  mo.  time  without 
interest.    What  was  the  cash  value  of  the  horse,  money 
being  worth  6%  ? 

4.  A  farmer  has  a  cow  worth  $80.    What  must  be  the 
selling  price  when  she  is  sold  on  3  mo.  time  without  inter- 
est, money  being  worth  6%  ? 

5.  I  bought  goods  at  a  credit  store  to   the  amount  of 
$82.40  on  6  mo.  time.    I  was  offered  a  5%  discount  for  cash. 
Did  I  gain  or  lose  by  accepting  the  offer,  money  being 
worth  6%  ? 

6.  A  merchant  who  conducts  a  credit  store  sold  during 
the  year  $20,000  worth  of  goods.   He  marked  his  goods  to 
sell  on  the  following  conditions;  namely,  10%  net  profit; 
6  mo.  time,  money  being  worth  6%  ;  2%  loss  on  bad  debts. 
What  was  the  selling  price  of  $1  worth  of  goods  ?   What  was 
a  cash  customer's  loss  on  purchases  amounting  to  $330  ? 

STATE  AND  LOCAL  TAXES 

137.  The  state  must  provide  for  taking  care  of  the  insane, 
the  blind,  the  deaf  and  dumb,  other  unfortunates,  and  the 
criminals ;  it  aids  in  supporting  schools  to  educate  the 
children ;  it  must  pay  the  salaries  of  the  governor  and 
other  state  officials,  and  look  after  general  improvements  — 
all  of  which  is  worth  many  more  thousands  of  dollars  to  the 


116  BUSINESS  PROBLEMS 

people  than  it  costs.  The  large  sum  of  money  required  to 
do  all  this  is  obtained  by  taxing  the  property  of  the  people. 
The  county  has  need  of  much  money  with  which  to  edu- 
cate its  people,  build  bridges,  roads,  courthouses,  school- 
houses,  take  care  of  its  poor,  and  maintain  courts  of  justice. 
These  expenses  are  all  met  by  taxing  the  people  and  their 
property. 

138.  A  poll  tax  is  a  tax  paid  by  each  male  citizen  over 
21  years  of  age  without  regard  to  how  little  or  how  much 
property  he  owns. 

Real  estate  is  any  fixed  property,  as  land  and  buildings. 
Personal  property  is  any  movable  property,  as  money, 
household  goods,  farming  implements,  cattle,  etc. 

139.  Property  tax  is  usually  listed  at  so  much  per  $100 
valuation  of  property. 

EXERCISE 

1.  How  much  tax  does  a  farmer  pay  who  owns  80  A.  of 
land  valued  at  $30  an  acre,  assessed  at  two  thirds  of  its 
value,  and  personal  property  assessed  at  $600,  if  the  rate  of 
taxation  is  $1.50  per  hundred?  $1.14  per  hundred? 

2.  How  much  tax  does  a  farmer  pay  who  owns  360  A.  of 
land  assessed  at  $3600,  and  personal  property  assessed  at 
$900,  if  the  rate  of  taxation  is  $1.50  per  hundred  ? 

3.  How  much  does  the  administration  of  justice  cost  a 
county  which  pays  annually  on  an  average  for  1944  da.  of 
jury  service  at  $2  per  day  and  for  2^-  mo.  of  a  circuit  judge's 
time  at  the  rate  of  $4200  a  year  ? 

4.  It  is  estimated  by  the  circuit  judge  presiding  in  the 
county  mentioned  in  problem  3  that  nine  tenths   of  the 
expense  was  incurred  in  prosecuting  crime  of  which  whisky 
and  ignorance  were  the  direct  cause.    If  this  expense  were 
to  be  met  by  a  poll  tax  on  the  1343  farmers  in  the  county, 
how  much  would  be  the  share  of  each  ? 


STATE  AND  LOCAL  TAXES  117 

5.  How  many  $800  schoolhouses  or  churches  could  be 
built  each  year  out  of  this  waste  ? 

6.  Estimate  the  rate  of  local  tax  on  the  $100  valuation 
necessary  to  make  $50  worth  of  repairs  on  the  schoolhouse 
and  to  buy  a  $25  library. 

NOTE.  The  advanced  pupils,  assisted  by  the  teacher,  might,  with 
interest,  make  a  list  of  the  taxable  property  in  their  district  —  the 
number  of  acres  of  land  and  its  value,  the  number  of  head  of  cattle, 
horses,  sheep,  etc.,  with  the  value  of  each.  Such  a  list  is  called  an 
assessment  roll. 


TABLES  OF  WEIGHTS  AND  MEASURES 

Long  Measure 
12  inches  =  1  foot 

3  feet  =  1  yard 
5^-  yards,  or  16^  feet  =  1  rod 

320  rods  =  1  mile 

Surveyor's  Measure 
7.92  inches  =  1  link 
25  links  =  1  rod 
4  rods,  or  100  links  =  1  chain 
80  chains  =  1  mile 

Square  Measure 

144  square  inches  ==  1  square  foot 
9  square  feet  =  1  square  yard 
30^  square  yards  =  1  square  rod 
160  square  rods  =  1  acre 

640  acres  =  1  square  mile 

Cubic  Measure 

1728  cubic  inches  —  1  cubic  foot 
27  cubic  feet  =  1  cubic  yard 
128  cubic  feet  =  1  cord 
1  cubic  yard  =  1  load  of  earth 

Liquid  Measure 

4  gills  =  1  pint 
2  pints  =  1  quart 

4  quarts  =  1  gallon 

=  231  cubic  inches 
118 


TABLES 


119 


Dry  Measure 
2  pints  =  1  quart 
8  quarts  =  1  peck 
4  pecks  =  1  bushel 

=  2150.42  cubic  inches 

A  heaped  bushel,  used  for  measuring  apples,  corn  in  the 
ear,  etc.,  equals  2747.71  cu.  in.  A  dry  quart  equals  67.2  cu.  in. 
and  a  liquid  quart  57.75  cu.  in. 

Avoirdupois  Weight 
16  ounces  =  1  pound 
100  pounds  =  1  hundredweight 
2000  pounds  =  1  ton 

Troy  Weight 

24  grains  =  1  pennyweight 
20  pennyweights  =  1  ounce 
12  ounces  =  1  pound 


WEIGHT  OF  GRAINS,  SEEDS,  AND  PRODUCE  USED  IN 
MOST  STATES 


Articles 

Pounds  per 
bushel 

Articles 

Pounds  per 
bushel 

Wheat    

60 

Rve  . 

56 

Beans     

60 

Blue-grass  seed 

14 

Corn,  shelled     .    .    . 
Corn,  on  cob  .... 

66 
70 

Buckwheat  .... 
Clover  "  

52 
60 

Oats  

32 

Flaxseed 

56 

Potatoes     

60 

Sweet  potatoes 

55 

Timothy  seed     .    .    . 
Onions   

45 
57 

Green  apples    .    .    . 
Dried  apples 

50 
24 

196  pounds  of  flour  =  1  barrel 

280  pounds  of  salt  =  1  barrel 

80  pounds  of  coal  =  1  bushel 


YB 


911242 


163 


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